{ "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 \u00d7 CT multiply \u00b7 level 0", "metric": "depth-aware-ckks-operation-latency", "operation": "multiply" } }, "failure": null, "finished_at": "2026-08-14T15:15:51.021059+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": 4.634564257482934e-06, "rms_error": 5.48002322868988e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-0-semantic-error", "observed": 2.59285624844775e-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": 4.658236791998001e-06, "rms_error": 5.508014218094136e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-0-semantic-error", "observed": 2.609194500549179e-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": 2.609194500549179e-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": 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"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": 2.609230481750786e-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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"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": 5.039590615947959e-06, "rms_error": 5.958936397071637e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-0-semantic-error", "observed": 2.606514313315789e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rescale_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rescale_to_next_level-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "rescale_to_next_level", "relative_l2_error": 4.658236791998001e-06, "rms_error": 5.508014218094136e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-0-semantic-error", "observed": 2.609194500549179e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": 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"name": "mod_switch_to_next_level-level-0-semantic-error", "observed": 2.609194500549179e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cpu", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": 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"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": 4.665025972538682e-06, "rms_error": 5.5160419128243684e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-1-semantic-error", "observed": 2.5668180061228473e-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": 4.665025972538682e-06, "rms_error": 5.5160419128243684e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-1-semantic-error", "observed": 2.5668180061228473e-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": 4.665025972538682e-06, "rms_error": 5.5160419128243684e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-1-semantic-error", "observed": 2.5668180061228473e-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": 6.013629992200959e-06, "rms_error": 8.865338143803856e-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": 3.7416652490723346e-06, "rms_error": 5.515990790415394e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-1-semantic-error", "observed": 2.566814433185059e-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": 4.883633522607826e-06, "rms_error": 5.201476236190102e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-1-semantic-error", "observed": 2.6176784855033545e-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": 8.358771025451249e-06, "rms_error": 8.902786962077798e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply-level-1-semantic-error", "observed": 4.954551106711867e-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": 8.358771025549847e-06, "rms_error": 8.902786962182824e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-1-semantic-error", "observed": 4.954551106860821e-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": 5.016238356540506e-06, "rms_error": 5.9313241088638356e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-1-semantic-error", "observed": 2.561311945789065e-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": 4.665025972538682e-06, "rms_error": 5.5160419128243684e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-1-semantic-error", "observed": 2.5668180061228473e-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": 4.665025972538682e-06, "rms_error": 5.5160419128243684e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-1-semantic-error", "observed": 2.5668180061228473e-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": 4.638173875133213e-06, "rms_error": 5.484291329739135e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-2-semantic-error", "observed": 2.5792411012005026e-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": 4.644382992312101e-06, "rms_error": 5.491633143225718e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-2-semantic-error", "observed": 2.601262714629351e-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": 4.644382992312101e-06, "rms_error": 5.491633143225718e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-2-semantic-error", "observed": 2.601262714629351e-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", 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6.0172000654131635e-06, "rms_error": 8.870601172334937e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-2-semantic-error", "observed": 5.178809868304639e-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": 4.8364371777681755e-06, "rms_error": 5.151208200109589e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-2-semantic-error", "observed": 2.6527967430344503e-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": 8.247327003640282e-06, "rms_error": 8.784089801770462e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply-level-2-semantic-error", "observed": 5.034556776114707e-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": 8.247327003747869e-06, "rms_error": 8.78408980188507e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-2-semantic-error", "observed": 5.0345567762672526e-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": 5.00358030631602e-06, "rms_error": 5.916356917687643e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-2-semantic-error", "observed": 2.6135831632215032e-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": 4.644382992312101e-06, "rms_error": 5.491633143225718e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-2-semantic-error", "observed": 2.601262714629351e-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": 4.644382992312101e-06, "rms_error": 5.491633143225718e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-2-semantic-error", "observed": 2.601262714629351e-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": 4.626034194901971e-06, "rms_error": 5.4699370720441184e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-3-semantic-error", "observed": 2.5937933014844755e-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": 4.658091131696658e-06, "rms_error": 5.507841985756747e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-3-semantic-error", "observed": 2.6008357328042618e-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": 4.658091131696658e-06, "rms_error": 5.507841985756747e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-3-semantic-error", "observed": 2.6008357328042618e-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": 4.658091131696658e-06, "rms_error": 5.507841985756747e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-3-semantic-error", "observed": 2.6008357328042618e-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": 3.7361507901844523e-06, "rms_error": 5.507861334033051e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-3-semantic-error", "observed": 2.6008452526368396e-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, 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"relative_l2_error": 4.846581814426854e-06, "rms_error": 5.162013082634162e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-3-semantic-error", "observed": 2.652340266869911e-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", 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"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": 8.286106343889025e-06, "rms_error": 8.825393027294097e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-3-semantic-error", "observed": 4.953342259837974e-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": 5.043410042575155e-06, "rms_error": 5.963452581436444e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-3-semantic-error", "observed": 2.5943803399098134e-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": 4.658091131696658e-06, "rms_error": 5.507841985756747e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-3-semantic-error", "observed": 2.6008357328042618e-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": 4.658091131696658e-06, "rms_error": 5.507841985756747e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-3-semantic-error", "observed": 2.6008357328042618e-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": 4.6174739070402745e-06, "rms_error": 5.4598151762799824e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-4-semantic-error", "observed": 2.6068397104696065e-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": 4.635067476915197e-06, "rms_error": 5.4806182477736025e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-4-semantic-error", "observed": 2.525191215778286e-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": 2.525191215778286e-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": 5.983180396802563e-06, "rms_error": 8.82044912337879e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-4-semantic-error", "observed": 5.116790413135526e-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": 3.717638787761451e-06, "rms_error": 5.480570802122762e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-4-semantic-error", "observed": 2.5251585083503928e-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": 4.840053438982457e-06, "rms_error": 5.155059819335894e-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": 8.234684930060144e-06, "rms_error": 8.770624941027168e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply-level-4-semantic-error", "observed": 4.9548517930035305e-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": 8.234684930163106e-06, "rms_error": 8.770624941136836e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-4-semantic-error", "observed": 4.9548517931519816e-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": 4.98113847518724e-06, "rms_error": 5.889821142359578e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-4-semantic-error", "observed": 2.514336357164876e-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": 4.635067476915197e-06, "rms_error": 5.4806182477736025e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-4-semantic-error", "observed": 2.525191215778286e-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": 4.635067476915197e-06, "rms_error": 5.4806182477736025e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-4-semantic-error", "observed": 2.525191215778286e-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": 4.592757846337153e-06, "rms_error": 5.43059029574109e-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": 4.629736396137334e-06, "rms_error": 5.4743146462107304e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-5-semantic-error", "observed": 2.5789186345811565e-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": 4.629736396137334e-06, "rms_error": 5.4743146462107304e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-5-semantic-error", "observed": 2.5789186345811565e-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": 4.629736396137334e-06, "rms_error": 5.4743146462107304e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-5-semantic-error", "observed": 2.5789186345811565e-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": 5.987277378328556e-06, "rms_error": 8.826488924072201e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-5-semantic-error", "observed": 5.1643414142606654e-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": 3.7133685537031035e-06, "rms_error": 5.4742755912552e-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 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"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": 8.296261785726773e-06, "rms_error": 8.836209418233863e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply-level-5-semantic-error", "observed": 5.021981752576376e-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": 8.296261785825009e-06, "rms_error": 8.836209418338488e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-5-semantic-error", "observed": 5.02198175272011e-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": 5.018564739417803e-06, "rms_error": 5.934074881428009e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-5-semantic-error", "observed": 2.576949506837591e-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": 4.629736396137334e-06, "rms_error": 5.4743146462107304e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-5-semantic-error", "observed": 2.5789186345811565e-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": 4.629736396137334e-06, "rms_error": 5.4743146462107304e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-5-semantic-error", "observed": 2.5789186345811565e-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": 4.627101246590012e-06, "rms_error": 5.471198780310913e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-6-semantic-error", "observed": 2.543311244020643e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 6, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 6, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" }, "operation": "decrypt", "predicted_exit_state": { "batch_shape": [], "component_count": null, "device": "cpu", "dtype": "torch.float64", "level": 6, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "decrypt-level-6-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 6, "nonfinite_count": 0, "operation": "decrypt", "relative_l2_error": 4.668900020988432e-06, "rms_error": 5.5206226833810377e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-6-semantic-error", "observed": 2.6144922345006423e-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": 4.668900020988432e-06, "rms_error": 5.5206226833810377e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-6-semantic-error", "observed": 2.6144922345006423e-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": 4.668900020988432e-06, "rms_error": 5.5206226833810377e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-6-semantic-error", "observed": 2.6144922345006423e-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": 6.077736903847178e-06, "rms_error": 8.959845030631909e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-6-semantic-error", "observed": 5.243648297423449e-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": 3.744794953312348e-06, "rms_error": 5.520604623726368e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-6-semantic-error", "observed": 2.6144406695455493e-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": 4.872911074684329e-06, "rms_error": 5.190055936568995e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-6-semantic-error", "observed": 2.6662692779241145e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 6, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply", "predicted_exit_state": { "batch_shape": [], "component_count": 3, "device": "cpu", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply-level-6-exit-state", "observed": 0, "oracle": "Observed 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", "relative_l2_error": 8.30953981910742e-06, "rms_error": 8.850351629104724e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply-level-6-semantic-error", "observed": 5.0891812721065096e-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": 2, "device": "cpu", "dtype": "torch.int64", 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