{ "benchmark_version": "v1", "cases": [ { "benchmark": "ckks-depth-aware-single-operations", "category": "Single operations", "comparison": { "axis": [ "operation", "entry_level" ], "portal_highlight": { "entry_level": 0, "label": "CT × CT multiply · level 0", "metric": "depth-aware-ckks-operation-latency", "operation": "multiply" } }, "failure": null, "finished_at": "2026-08-14T15:30:05.371673+00:00", "id": "ckks-depth-aware-single-operations", "parameters": { "ciphertext_modulus_basis": "Q", "include_raw_samples": true, "levels": [ 0, 1, 2, 3, 4, 5, 6 ], "logN": 14, "nonce": 0, "ntt_backend": "radix2_indexed", "num_p_primes": 1, "num_scale_primes": 7, "operations": [ "encrypt", "decrypt", "coefficient_domain_to_ntt_domain", "ntt_domain_to_coefficient_domain", "add", "add_plaintext", "multiply_plaintext", "multiply", "relinearize", "rotate_with_key", "rescale_to_next_level", "mod_switch_to_next_level" ], "preset": "slots8192-scale40-levels7-int64", "rescale_rounding": "nearest", "rotation_step": 1, "runs": 3, "scale_bits": 40, "seed": 20260807, "warmup": 1 }, "profile": "core", "requirements": { "native_backends_any": [ "cpu", "cuda" ] }, "result": { "benchmark": "ckks-depth-aware-single-operations", "correctness": [ { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "encrypt-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "encrypt", "relative_l2_error": 4.63456425748005e-06, "rms_error": 5.4800232286864736e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-0-semantic-error", "observed": 2.5928562484449522e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 0, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" }, "operation": "decrypt", "predicted_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 0, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "decrypt-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "decrypt", "relative_l2_error": 4.658236791994558e-06, "rms_error": 5.508014218090064e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-0-semantic-error", "observed": 2.6091945005488633e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "coefficient_domain_to_ntt_domain", 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"coefficient_domain_to_ntt_domain-level-0-semantic-error", "observed": 2.6091945005488633e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "ntt_domain_to_coefficient_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "ntt_domain_to_coefficient_domain-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "ntt_domain_to_coefficient_domain", "relative_l2_error": 4.658236791994558e-06, "rms_error": 5.508014218090064e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-0-semantic-error", "observed": 2.6091945005488633e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual 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"add_plaintext-level-0-semantic-error", "observed": 2.6092304817540646e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": 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"relinearize-level-0-semantic-error", "observed": 5.013799912500039e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rotate_with_key", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rotate_with_key-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "rotate_with_key", "relative_l2_error": 5.039590615942345e-06, "rms_error": 5.958936397065001e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-0-semantic-error", "observed": 2.6065143133136683e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rescale_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rescale_to_next_level-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "rescale_to_next_level", "relative_l2_error": 4.658236791994558e-06, "rms_error": 5.508014218090064e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-0-semantic-error", "observed": 2.6091945005488633e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": 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"name": "mod_switch_to_next_level-level-0-semantic-error", "observed": 2.6091945005488633e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": 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"cpu", "dtype": "torch.float64", "level": 1, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" }, "operation": "decrypt", "predicted_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 1, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "decrypt-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "decrypt", "relative_l2_error": 4.665025972536661e-06, "rms_error": 5.516041912821975e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-1-semantic-error", "observed": 2.5668180061225606e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "coefficient_domain_to_ntt_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "coefficient_domain_to_ntt_domain-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "coefficient_domain_to_ntt_domain", "relative_l2_error": 4.665025972536661e-06, "rms_error": 5.516041912821975e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-1-semantic-error", "observed": 2.5668180061225606e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "ntt_domain_to_coefficient_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "ntt_domain_to_coefficient_domain-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "ntt_domain_to_coefficient_domain", "relative_l2_error": 4.665025972536661e-06, "rms_error": 5.516041912821975e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-1-semantic-error", "observed": 2.5668180061225606e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "add", "relative_l2_error": 6.013629992200102e-06, "rms_error": 8.865338143802583e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-1-semantic-error", "observed": 5.100981524853185e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add_plaintext-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "add_plaintext", "relative_l2_error": 3.741665249071353e-06, "rms_error": 5.515990790413954e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-1-semantic-error", "observed": 2.5668144331822987e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply_plaintext-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "multiply_plaintext", "relative_l2_error": 4.883633522607445e-06, "rms_error": 5.20147623618969e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-1-semantic-error", "observed": 2.617678485503195e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply", "predicted_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "multiply", "relative_l2_error": 8.35877102545195e-06, "rms_error": 8.902786962078543e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply-level-1-semantic-error", "observed": 4.954551106713819e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "relinearize", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "relinearize-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "relinearize", "relative_l2_error": 8.358771025549483e-06, "rms_error": 8.902786962182426e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-1-semantic-error", "observed": 4.9545511068618495e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rotate_with_key", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rotate_with_key-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "rotate_with_key", "relative_l2_error": 5.016238356539411e-06, "rms_error": 5.931324108862538e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-1-semantic-error", "observed": 2.5613119457895516e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rescale_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rescale_to_next_level-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "rescale_to_next_level", "relative_l2_error": 4.665025972536661e-06, "rms_error": 5.516041912821975e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-1-semantic-error", "observed": 2.5668180061225606e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "mod_switch_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "mod_switch_to_next_level-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "mod_switch_to_next_level", "relative_l2_error": 4.665025972536661e-06, "rms_error": 5.516041912821975e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-1-semantic-error", "observed": 2.5668180061225606e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "encrypt-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "encrypt", "relative_l2_error": 4.638173875130623e-06, "rms_error": 5.48429132973608e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-2-semantic-error", "observed": 2.579241101198615e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 2, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" }, "operation": "decrypt", "predicted_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 2, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "decrypt-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "decrypt", "relative_l2_error": 4.644382992312794e-06, "rms_error": 5.49163314322653e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-2-semantic-error", "observed": 2.6012627146301705e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "coefficient_domain_to_ntt_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "coefficient_domain_to_ntt_domain-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "coefficient_domain_to_ntt_domain", "relative_l2_error": 4.644382992312794e-06, "rms_error": 5.49163314322653e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-2-semantic-error", "observed": 2.6012627146301705e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "ntt_domain_to_coefficient_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "ntt_domain_to_coefficient_domain-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "ntt_domain_to_coefficient_domain", "relative_l2_error": 4.644382992312794e-06, "rms_error": 5.49163314322653e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-2-semantic-error", "observed": 2.6012627146301705e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "add", "relative_l2_error": 6.017200065413051e-06, "rms_error": 8.870601172334757e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-2-semantic-error", "observed": 5.1788098683079135e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add_plaintext-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "add_plaintext", "relative_l2_error": 3.725161983746938e-06, "rms_error": 5.491661553702087e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-2-semantic-error", "observed": 2.6012490067993012e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply_plaintext-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "multiply_plaintext", "relative_l2_error": 4.836437177773844e-06, "rms_error": 5.151208200115613e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-2-semantic-error", "observed": 2.6527967430376237e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply", "predicted_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "multiply", "relative_l2_error": 8.247327003644776e-06, "rms_error": 8.784089801775263e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply-level-2-semantic-error", "observed": 5.0345567761157144e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "relinearize", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "relinearize-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "relinearize", "relative_l2_error": 8.247327003749122e-06, "rms_error": 8.784089801886405e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-2-semantic-error", "observed": 5.034556776265643e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rotate_with_key", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rotate_with_key-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "rotate_with_key", "relative_l2_error": 5.003580306314993e-06, "rms_error": 5.916356917686426e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-2-semantic-error", "observed": 2.613583163220979e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rescale_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rescale_to_next_level-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "rescale_to_next_level", "relative_l2_error": 4.644382992312794e-06, "rms_error": 5.49163314322653e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-2-semantic-error", "observed": 2.6012627146301705e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "mod_switch_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "mod_switch_to_next_level-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "mod_switch_to_next_level", "relative_l2_error": 4.644382992312794e-06, "rms_error": 5.49163314322653e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-2-semantic-error", "observed": 2.6012627146301705e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "encrypt-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "encrypt", "relative_l2_error": 4.626034194911054e-06, "rms_error": 5.469937072054849e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-3-semantic-error", "observed": 2.593793301486121e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 3, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" }, "operation": "decrypt", "predicted_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 3, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "decrypt-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "decrypt", "relative_l2_error": 4.6580911316978785e-06, "rms_error": 5.507841985758189e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-3-semantic-error", "observed": 2.600835732805084e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "coefficient_domain_to_ntt_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "coefficient_domain_to_ntt_domain-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "coefficient_domain_to_ntt_domain", "relative_l2_error": 4.6580911316978785e-06, "rms_error": 5.507841985758189e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-3-semantic-error", "observed": 2.600835732805084e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "ntt_domain_to_coefficient_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "ntt_domain_to_coefficient_domain-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "ntt_domain_to_coefficient_domain", "relative_l2_error": 4.6580911316978785e-06, "rms_error": 5.507841985758189e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-3-semantic-error", "observed": 2.600835732805084e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "add", "relative_l2_error": 6.010214768318761e-06, "rms_error": 8.860303395308891e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-3-semantic-error", "observed": 5.12752306120588e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add_plaintext-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "add_plaintext", "relative_l2_error": 3.736150790182081e-06, "rms_error": 5.5078613340295565e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-3-semantic-error", "observed": 2.6008452526379462e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply_plaintext-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "multiply_plaintext", "relative_l2_error": 4.846581814424919e-06, "rms_error": 5.162013082632108e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-3-semantic-error", "observed": 2.6523402668702394e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply", "predicted_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "multiply", "relative_l2_error": 8.286106343782894e-06, "rms_error": 8.82539302718105e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply-level-3-semantic-error", "observed": 4.953342259691078e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "relinearize", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "relinearize-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "relinearize", "relative_l2_error": 8.286106343883789e-06, "rms_error": 8.825393027288515e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-3-semantic-error", "observed": 4.953342259838352e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rotate_with_key", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rotate_with_key-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "rotate_with_key", "relative_l2_error": 5.043410042575847e-06, "rms_error": 5.963452581437263e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-3-semantic-error", "observed": 2.5943803399111864e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rescale_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rescale_to_next_level-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "rescale_to_next_level", "relative_l2_error": 4.6580911316978785e-06, "rms_error": 5.507841985758189e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-3-semantic-error", "observed": 2.600835732805084e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "mod_switch_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "mod_switch_to_next_level-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "mod_switch_to_next_level", "relative_l2_error": 4.6580911316978785e-06, "rms_error": 5.507841985758189e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-3-semantic-error", "observed": 2.600835732805084e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "encrypt-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "encrypt", "relative_l2_error": 4.6174739070434474e-06, "rms_error": 5.4598151762837444e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-4-semantic-error", "observed": 2.606839710471794e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 4, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" }, "operation": "decrypt", "predicted_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 4, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "decrypt-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "decrypt", "relative_l2_error": 4.635067476911232e-06, "rms_error": 5.480618247768913e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-4-semantic-error", "observed": 2.52519121577946e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "coefficient_domain_to_ntt_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "coefficient_domain_to_ntt_domain-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "coefficient_domain_to_ntt_domain", "relative_l2_error": 4.635067476911232e-06, "rms_error": 5.480618247768913e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-4-semantic-error", "observed": 2.52519121577946e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "ntt_domain_to_coefficient_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "ntt_domain_to_coefficient_domain-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "ntt_domain_to_coefficient_domain", "relative_l2_error": 4.635067476911232e-06, "rms_error": 5.480618247768913e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-4-semantic-error", "observed": 2.52519121577946e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "add", "relative_l2_error": 5.983180396799472e-06, "rms_error": 8.820449123374224e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-4-semantic-error", "observed": 5.116790413136101e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add_plaintext-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "add_plaintext", "relative_l2_error": 3.7176387877570674e-06, "rms_error": 5.480570802116305e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-4-semantic-error", "observed": 2.5251585083536577e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "ntt", 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"details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply", "predicted_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "multiply", "relative_l2_error": 8.234684930058861e-06, "rms_error": 8.770624941025801e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply-level-4-semantic-error", "observed": 4.9548517930041836e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "relinearize", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "relinearize-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "relinearize", "relative_l2_error": 8.234684930161442e-06, "rms_error": 8.770624941135066e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-4-semantic-error", "observed": 4.954851793153941e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rotate_with_key", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rotate_with_key-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "rotate_with_key", "relative_l2_error": 4.981138475183685e-06, "rms_error": 5.8898211423553723e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-4-semantic-error", "observed": 2.5143363571630084e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rescale_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rescale_to_next_level-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "rescale_to_next_level", "relative_l2_error": 4.635067476911232e-06, "rms_error": 5.480618247768913e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-4-semantic-error", "observed": 2.52519121577946e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "mod_switch_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "mod_switch_to_next_level-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "mod_switch_to_next_level", "relative_l2_error": 4.635067476911232e-06, "rms_error": 5.480618247768913e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-4-semantic-error", "observed": 2.52519121577946e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "encrypt-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 5, "nonfinite_count": 0, "operation": "encrypt", "relative_l2_error": 4.592757846337952e-06, "rms_error": 5.4305902957420324e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-5-semantic-error", "observed": 2.570102797947974e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 5, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" }, "operation": "decrypt", "predicted_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 5, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "decrypt-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 5, "nonfinite_count": 0, "operation": "decrypt", "relative_l2_error": 4.629736396139503e-06, "rms_error": 5.474314646213292e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-5-semantic-error", "observed": 2.578918634582537e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "coefficient_domain_to_ntt_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "coefficient_domain_to_ntt_domain-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 5, "nonfinite_count": 0, "operation": "coefficient_domain_to_ntt_domain", "relative_l2_error": 4.629736396139503e-06, "rms_error": 5.474314646213292e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-5-semantic-error", "observed": 2.578918634582537e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "ntt_domain_to_coefficient_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "ntt_domain_to_coefficient_domain-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 5, "nonfinite_count": 0, "operation": "ntt_domain_to_coefficient_domain", "relative_l2_error": 4.629736396139503e-06, "rms_error": 5.474314646213292e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-5-semantic-error", "observed": 2.578918634582537e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 5, "nonfinite_count": 0, "operation": "add", "relative_l2_error": 5.987277378327027e-06, "rms_error": 8.826488924069942e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-5-semantic-error", "observed": 5.164341414261231e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add_plaintext-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 5, "nonfinite_count": 0, "operation": "add_plaintext", "relative_l2_error": 3.7133685536991084e-06, "rms_error": 5.474275591249312e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-5-semantic-error", "observed": 2.578914032154506e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply_plaintext-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 5, "nonfinite_count": 0, "operation": "multiply_plaintext", "relative_l2_error": 4.842851109917572e-06, "rms_error": 5.158039571771929e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-5-semantic-error", "observed": 2.6299747952225677e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply", 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slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "relinearize", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "relinearize-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 5, "nonfinite_count": 0, "operation": "relinearize", "relative_l2_error": 8.29626178582453e-06, "rms_error": 8.836209418337973e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-5-semantic-error", "observed": 5.021981752722502e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rotate_with_key", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 5, "limb_count": 3, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rotate_with_key-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 5, "nonfinite_count": 0, "operation": "rotate_with_key", "relative_l2_error": 5.01856473942359e-06, "rms_error": 5.934074881434859e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-5-semantic-error", "observed": 2.576949506843096e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rescale_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rescale_to_next_level-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 5, "nonfinite_count": 0, "operation": "rescale_to_next_level", "relative_l2_error": 4.629736396139503e-06, "rms_error": 5.474314646213292e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-5-semantic-error", "observed": 2.578918634582537e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "mod_switch_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "mod_switch_to_next_level-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 5, "nonfinite_count": 0, "operation": "mod_switch_to_next_level", "relative_l2_error": 4.629736396139503e-06, "rms_error": 5.474314646213292e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-5-semantic-error", "observed": 2.578918634582537e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 6, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "encrypt-level-6-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 6, "nonfinite_count": 0, "operation": "encrypt", "relative_l2_error": 4.6271012465904e-06, "rms_error": 5.4711987803113746e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-6-semantic-error", "observed": 2.543311244020643e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 6, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 6, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" }, "operation": "decrypt", "predicted_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 6, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "decrypt-level-6-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 6, "nonfinite_count": 0, "operation": "decrypt", "relative_l2_error": 4.668900020990605e-06, "rms_error": 5.5206226833836105e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-6-semantic-error", "observed": 2.6144922345022792e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 6, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "coefficient_domain_to_ntt_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "coefficient_domain_to_ntt_domain-level-6-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 6, "nonfinite_count": 0, "operation": "coefficient_domain_to_ntt_domain", "relative_l2_error": 4.668900020990605e-06, "rms_error": 5.5206226833836105e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-6-semantic-error", "observed": 2.6144922345022792e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 6, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "ntt_domain_to_coefficient_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "ntt_domain_to_coefficient_domain-level-6-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 6, "nonfinite_count": 0, "operation": "ntt_domain_to_coefficient_domain", "relative_l2_error": 4.668900020990605e-06, "rms_error": 5.5206226833836105e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-6-semantic-error", "observed": 2.6144922345022792e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 6, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add-level-6-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 6, "nonfinite_count": 0, "operation": "add", "relative_l2_error": 6.077736903848699e-06, "rms_error": 8.959845030634141e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-6-semantic-error", "observed": 5.2436482974240216e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 6, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add_plaintext-level-6-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 6, "nonfinite_count": 0, "operation": "add_plaintext", "relative_l2_error": 3.7447949533174857e-06, "rms_error": 5.5206046237339346e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-6-semantic-error", "observed": 2.6144406695478473e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 6, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply_plaintext-level-6-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 6, "nonfinite_count": 0, "operation": "multiply_plaintext", "relative_l2_error": 4.8729110746820255e-06, "rms_error": 5.190055936566541e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-6-semantic-error", "observed": 2.6662692779228754e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 6, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply", "predicted_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply-level-6-exit-state", "observed": 0, "oracle": "Observed 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"modulus_decimal": "1099510054913", "prime_id": 0, "role": "scale_q_prime" }, { "modulus_bits": 41, "modulus_decimal": "1099515691009", "prime_id": 1, "role": "scale_q_prime" }, { "modulus_bits": 40, "modulus_decimal": "1099508121601", "prime_id": 2, "role": "scale_q_prime" }, { "modulus_bits": 41, "modulus_decimal": "1099515789313", "prime_id": 3, "role": "scale_q_prime" }, { "modulus_bits": 40, "modulus_decimal": "1099507695617", "prime_id": 4, "role": "scale_q_prime" }, { "modulus_bits": 41, "modulus_decimal": "1099516280833", "prime_id": 5, "role": "scale_q_prime" }, { "modulus_bits": 40, "modulus_decimal": "1099506515969", "prime_id": 6, "role": "scale_q_prime" }, { "modulus_bits": 60, "modulus_decimal": "1152921504606748673", "prime_id": 7, "role": "structural_base_q_prime" } ], "ring_dimension": 16384, "scale_bits": 40, "security_bits": 128, "security_budget_enforced": true, "sigma": 3.19, "torch_dtype": "torch.int64" }, "entry_state": { "axis": "public_source_level", "construction": "direct_at_entry_level", "entry_chain_depth_definition": "The number of leading scale-Q rows absent relative to Q_0; for a public FHElium value it equals entry_level and does not assert that the setup executed that many multiplications.", "levels": [ { "active_q_count": 8, "active_q_prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "active_q_product_bits": 340, "active_scale_prime_count": 7, "available_public_transitions": 6, "entry_chain_depth": 0, "entry_level": 0 }, { "active_q_count": 7, "active_q_prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "active_q_product_bits": 301, "active_scale_prime_count": 6, "available_public_transitions": 5, "entry_chain_depth": 1, "entry_level": 1 }, { "active_q_count": 6, "active_q_prime_ids": [ 2, 3, 4, 5, 6, 7 ], "active_q_product_bits": 260, "active_scale_prime_count": 5, "available_public_transitions": 4, "entry_chain_depth": 2, "entry_level": 2 }, { "active_q_count": 5, "active_q_prime_ids": [ 3, 4, 5, 6, 7 ], "active_q_product_bits": 220, "active_scale_prime_count": 4, "available_public_transitions": 3, "entry_chain_depth": 3, "entry_level": 3 }, { "active_q_count": 4, "active_q_prime_ids": [ 4, 5, 6, 7 ], "active_q_product_bits": 180, "active_scale_prime_count": 3, "available_public_transitions": 2, "entry_chain_depth": 4, "entry_level": 4 }, { "active_q_count": 3, "active_q_prime_ids": [ 5, 6, 7 ], "active_q_product_bits": 140, "active_scale_prime_count": 2, "available_public_transitions": 1, "entry_chain_depth": 5, "entry_level": 5 }, { "active_q_count": 2, "active_q_prime_ids": [ 6, 7 ], "active_q_product_bits": 100, "active_scale_prime_count": 1, "available_public_transitions": 0, "entry_chain_depth": 6, "entry_level": 6 } ], "multiplicative_history_definition": "Workload multiplicative depth before entry and depth added by the timed call are reported separately from public level." }, "parameter_selection": { "complete_qp_product_bits": 400, "maximum_security_budget_bits": 430, "rationale": "The maintained slots8192-scale40-levels7-int64 preset fixes logN=14, 8,192 complex slots, seven public levels, one key-switch P prime, and an enforced 128-bit security-table budget. The indexed radix-2 backend is the one fixed implementation shared by CPU and CUDA.", "security_budget_status": "within_exact_builtin_budget" } }, "key_bytes_by_role": { "decryption_key": 1179648, "public_key": 2097152, "relinearization_key": 18874368, "rotation_key_step_1": 18874368 }, "level_order": [ 0, 1, 2, 3, 4, 5, 6 ], "not_applicable_cases": [ { "active_q_count": 2, "active_q_prime_ids": [ 6, 7 ], "active_q_product_bits": 100, "active_scale_prime_count": 1, "available_public_transitions": 0, "entry_chain_depth": 6, "entry_level": 6, "observed_exit_state": null, "operation": "rescale_to_next_level", "predicted_exit_state": null, "reason": "rescale_to_next_level requires a source below final_public_level=6; the terminal exception path is not timed.", "reason_code": "no_following_public_level", "status": "not_applicable" }, { "active_q_count": 2, "active_q_prime_ids": [ 6, 7 ], "active_q_product_bits": 100, "active_scale_prime_count": 1, "available_public_transitions": 0, "entry_chain_depth": 6, "entry_level": 6, "observed_exit_state": null, "operation": "mod_switch_to_next_level", "predicted_exit_state": null, "reason": "mod_switch_to_next_level requires a source below final_public_level=6; the terminal exception path is not timed.", "reason_code": "no_following_public_level", "status": "not_applicable" } ], "operation_order": [ "encrypt", "decrypt", "coefficient_domain_to_ntt_domain", "ntt_domain_to_coefficient_domain", "add", "add_plaintext", "multiply_plaintext", "multiply", "relinearize", "rotate_with_key", "rescale_to_next_level", "mod_switch_to_next_level" ], "resolved_parameters": { "ciphertext_modulus_basis": "Q", "default_scale": 1099511627776.0, "device": "cpu", "include_raw_samples": true, "levels": [ 0, 1, 2, 3, 4, 5, 6 ], "logN": 14, "nonce": 0, "ntt_backend": "radix2_indexed", "num_p_primes": 1, "num_scale_primes": 7, "num_slots": 8192, "operations": [ "encrypt", "decrypt", "coefficient_domain_to_ntt_domain", "ntt_domain_to_coefficient_domain", "add", "add_plaintext", "multiply_plaintext", "multiply", "relinearize", "rotate_with_key", "rescale_to_next_level", "mod_switch_to_next_level" ], "preset": "slots8192-scale40-levels7-int64", "rescale_rounding": "nearest", "rotation_step": 1, "runs": 3, "scale_bits": 40, "seed": 20260807, "warmup": 1 }, "timed_boundary": { "description": "One functional public CkksEngine call at one exact entry level, with synchronized device completion.", "excludes": [ "engine and native-table construction", "key generation or lookup", "cleartext input construction", "encoding and operation-ready plaintext preparation", "setup encryption and domain conversion", "pending-product construction for relinearization or rescale", "correctness decryption, decoding, and state validation", "cleanup" ], "id": "depth-aware-single-public-ckks-call", "includes": [ "one named functional public CkksEngine call", "output allocation and every representation conversion specified by that call" ], "synchronization": "Synchronize the selected engine device before each sample and after the public call; CPU calls complete synchronously. 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