{ "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": "2026-08-14T14:52:34.734983+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": 4.634564257479783e-06, "rms_error": 5.4800232286861553e-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": 4.658236791993984e-06, "rms_error": 5.508014218089387e-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": 4.658236791993984e-06, "rms_error": 5.508014218089387e-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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"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": 5.039590615942659e-06, "rms_error": 5.958936397065373e-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": 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true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "rescale_to_next_level", "relative_l2_error": 4.658236791993984e-06, "rms_error": 5.508014218089387e-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": "ciphertext" }, "operation": "mod_switch_to_next_level", 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"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" }, "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": 4.665025972536789e-06, "rms_error": 5.5160419128221264e-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": 4.665025972536789e-06, "rms_error": 5.5160419128221264e-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": 4.665025972536789e-06, "rms_error": 5.5160419128221264e-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": 6.013629992200581e-06, "rms_error": 8.865338143803292e-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": 3.741665249071003e-06, "rms_error": 5.5159907904134375e-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": 4.883633522606421e-06, "rms_error": 5.2014762361886e-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": 8.358771025452006e-06, "rms_error": 8.902786962078604e-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": 8.358771025549096e-06, "rms_error": 8.902786962182016e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-1-semantic-error", "observed": 4.954551106861199e-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": 5.0162383565392755e-06, "rms_error": 5.931324108862377e-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": 4.665025972536789e-06, "rms_error": 5.5160419128221264e-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": 4.665025972536789e-06, "rms_error": 5.5160419128221264e-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": 4.638173875130502e-06, "rms_error": 5.4842913297359365e-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": 4.644382992313234e-06, "rms_error": 5.491633143227051e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-2-semantic-error", "observed": 2.6012627146309905e-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": 4.644382992313234e-06, "rms_error": 5.491633143227051e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-2-semantic-error", "observed": 2.6012627146309905e-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": 4.644382992313234e-06, "rms_error": 5.491633143227051e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-2-semantic-error", "observed": 2.6012627146309905e-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", 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6.0172000654130915e-06, "rms_error": 8.870601172334824e-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", 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"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": 4.836437177774159e-06, "rms_error": 5.151208200115949e-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": 8.24732700364461e-06, "rms_error": 8.784089801775087e-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": 8.247327003749797e-06, "rms_error": 8.784089801887116e-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": 5.003580306314952e-06, "rms_error": 5.9163569176863766e-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": 4.644382992313234e-06, "rms_error": 5.491633143227051e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-2-semantic-error", "observed": 2.6012627146309905e-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": 4.644382992313234e-06, "rms_error": 5.491633143227051e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-2-semantic-error", "observed": 2.6012627146309905e-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": 4.62603419491067e-06, "rms_error": 5.4699370720543986e-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": 4.658091131697582e-06, "rms_error": 5.507841985757836e-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": 4.658091131697582e-06, "rms_error": 5.507841985757836e-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, 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"fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "ntt_domain_to_coefficient_domain", "relative_l2_error": 4.658091131697582e-06, "rms_error": 5.507841985757836e-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": { 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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": 3.736150790183273e-06, "rms_error": 5.507861334031313e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-3-semantic-error", "observed": 2.6008452526412344e-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": 4.8465818144249494e-06, "rms_error": 5.162013082632137e-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": 8.28610634378277e-06, "rms_error": 8.825393027180916e-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": 8.286106343884086e-06, "rms_error": 8.825393027288832e-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": 5.043410042575737e-06, "rms_error": 5.96345258143713e-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": 4.658091131697582e-06, "rms_error": 5.507841985757836e-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": 4.658091131697582e-06, "rms_error": 5.507841985757836e-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": 4.617473907043784e-06, "rms_error": 5.459815176284145e-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": 4.635067476911509e-06, "rms_error": 5.480618247769238e-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" }, { 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"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": 5.983180396799559e-06, "rms_error": 8.82044912337435e-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": 3.7176387877575524e-06, "rms_error": 5.4805708021170206e-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", "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_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": "multiply_plaintext", "relative_l2_error": 4.840053438983522e-06, "rms_error": 5.155059819337027e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-4-semantic-error", "observed": 2.57519530889596e-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": 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": 8.234684930058274e-06, "rms_error": 8.770624941025175e-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": 8.23468493016172e-06, "rms_error": 8.770624941135362e-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": 4.981138475183516e-06, "rms_error": 5.889821142355172e-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": 4.635067476911509e-06, "rms_error": 5.480618247769238e-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": 4.635067476911509e-06, "rms_error": 5.480618247769238e-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": 4.592757846337965e-06, "rms_error": 5.430590295742049e-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": 4.629736396139543e-06, "rms_error": 5.47431464621334e-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": 4.629736396139543e-06, "rms_error": 5.47431464621334e-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": 4.629736396139543e-06, "rms_error": 5.47431464621334e-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": 5.987277378326963e-06, "rms_error": 8.826488924069848e-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": 3.7133685536989505e-06, "rms_error": 5.474275591249077e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-5-semantic-error", "observed": 2.578914032153946e-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": 4.8428511099181696e-06, "rms_error": 5.158039571772563e-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", "predicted_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" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply-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", "relative_l2_error": 8.296261785722499e-06, "rms_error": 8.836209418229301e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply-level-5-semantic-error", "observed": 5.021981752578697e-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": 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": 8.29626178582454e-06, "rms_error": 8.836209418337983e-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": 5.018564739423446e-06, "rms_error": 5.934074881434687e-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": 4.629736396139543e-06, "rms_error": 5.47431464621334e-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": 4.629736396139543e-06, "rms_error": 5.47431464621334e-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": 4.627101246589492e-06, "rms_error": 5.471198780310297e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-6-semantic-error", "observed": 2.543311244019823e-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": 4.668900020990256e-06, "rms_error": 5.520622683383197e-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": 4.668900020990256e-06, "rms_error": 5.520622683383197e-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": 4.668900020990256e-06, "rms_error": 5.520622683383197e-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": 6.077736903848929e-06, "rms_error": 8.959845030634491e-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": 3.744794953317354e-06, "rms_error": 5.520604623733742e-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": 4.8729110746825185e-06, "rms_error": 5.190055936567066e-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": 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