Search: “algorithms”

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Hamming Ideals and Grobner Bases for ISD-like Syndrome Decoding

Researchers combine Grobner bases with Information Set Decoding for syndrome decoding, testing feasibility against Classic McEliece NIST Category 1 parameters.

The paper proposes GBDecode, an ISD-like decoding algorithm that fixes only a subset of an information set and solves the resulting multivariate nonlinear systems via MultiSolve, which replaces one Grobner basis computation with many computations on simpler systems. Hamming weight constraints are reformulated using elementary symmetric functions and Lucas' identity factorizations to bound equation degree. Experiments on random binary linear codes use parameters matching the NIST Security Category 1 set of the Classic McEliece cryptosystem, assessing practical feasibility rather than breaking the scheme.

arXiv cs.CRSep 16, 16:05 UTC · 13h agoResearch

A Global Readiness and Sovereignty Capability Model for Post-Quantum Cryptography Migration

Researchers propose a Readiness-Sovereignty Capability Model scoring 57 countries on post-quantum cryptography readiness and sovereignty.

The RSCM model decomposes cryptographic sovereignty into indigenous capacity, indigenous post-quantum control, and external dependency, with a gate requiring demonstrated creation in at least one core layer. Applied to 57 documented cryptographic actors, 20 countries clear the maker gate (15 full-stack, 5 research makers), 11 hold strong general capacity without post-quantum control, and 25 are dependent. Readiness correlates with independent cyber indices up to rank correlation 0.70, while post-quantum creation shows no significant correlation with commitment (0.22).

arXiv cs.CRSep 16, 11:10 UTC · 18h agoResearch

Witness Encryption via Prime-Order Generic Groups

Unconditional witness encryption construction for NP in the generic-group model, plus first superconstant NP-hardness result for homogeneous MinRank.

A cryptography paper unconditionally constructs witness encryption for NP in the classical generic-group model using an ordinary cyclic group of prime order. For SAT instances of size n, encryption and decryption run in poly(n) time with correctness error 2^-n^Ω(1), while generic adversaries making n^Θ(log n) queries achieve at most n^-Θ(log n) distinguishing advantage. It also proves the first superconstant-factor NP-hardness of approximation for homogeneous MinRank under randomized reductions.

arXiv cs.CRSep 16, 07:54 UTC · 21h agoResearch