Dependency-Aware ROM/CBD Correctness Bounds for ML-KEM-768 at the Heuristic Failure Scale
Researchers certify a dependency-preserving upper bound of 2^-164.81 on honest decapsulation failure for ML-KEM-768 within an explicit ROM/CBD abstraction.
The paper models ML-KEM-768's domain-separated public-matrix streams as independent uniform ring elements and secret polynomials as CBD2 primitives, explicitly not claiming an information-theoretic result about the fixed SHAKE instantiation in FIPS 203. It preserves dependencies from the public matrix and both ciphertext-compression terms, using a graph-coupled reference, a proper-ideal bivariate Fourier transport, and a 256-coordinate union bound. The certified bound is Pr[K' != K] <= 2^-164.81, with the exponent 164.8107162... exceeding the 164.81 threshold by only about 0.0007162 bits; 164.82 is not certified. The bound applies to messages fixed independently of the randomness under honest encryption and decapsulation, and is not an exact DFR, a fixed-SHAKE equivalence, or a new IND-CCA reduction.
- Certified upper bound of 2^-164.81 on honest decapsulation failure for ML-KEM-768.
- Analysis preserves dependencies from the public matrix and both ciphertext-compression terms.
- Bound is numerically tight: exponent exceeds 164.81 by about 0.0007162 bits.
- Result is abstraction-specific, not an exact DFR or fixed-SHAKE equivalence theorem.
Full article231 words · extracted from arxiv.org · click to collapse
We certify an honest-decapsulation failure upper bound for ML-KEM-768 in an explicit random-function/centered-binomial (ROM/CBD) abstraction. Domain-separated public-matrix streams are modeled as independent uniform ring elements and secret/noise polynomials as independent CBD2 primitives; this is not an information-theoretic statement about the fixed SHAKE instantiation of FIPS 203. Recent formal assessments identify rigorous justification of ML-KEM's heuristic decapsulation-failure scale as an open problem; within the explicit ROM/CBD abstraction studied here, we obtain a dependency-preserving certified upper bound at that scale. The analysis preserves dependencies induced by the public matrix and by both ciphertext-compression terms. Its terminal chain has three components: an exact graph-coupled full-ideal reference for the joint c_u/c_v residual; a proper-ideal bivariate Fourier transport whose rare |T|>=3 branch is closed by an exhaustive three-factor anti-concentration replay; and exact bit-specific FIPS decoding events followed only by a 256-coordinate union bound. A formal partial-Fourier lemma makes the spectral-to-total-variation step explicit. The reduced rational certificate satisfies Pr[K' != K] <= P_* <= 2^-164.81, with -log2(P_*) = 164.810716201343121.... The 164.81 threshold is exact but numerically tight: the certified exponent exceeds it by only about 0.0007162 bit, and 164.82 is not certified. The result is an upper bound for an arbitrary message fixed independently of the public and secret randomness, under honest encryption and decapsulation. It is not an exact DFR, not a fixed-SHAKE equivalence theorem, not a new IND-CCA reduction, and not an adaptive delta-correctness result.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.09983