Description
In the 1960s, Berlekamp introduced the negacyclic codes over GF(p) and described an efficient decoder that corrects any t Lee errors, where p > 2t. We consider this family of codes, defined over the integers modulo 4. We show that if a generator polynomial for a Z4 negacyclic code C has roots a^{2j+1} for j=0,...,t, where a is a primitive 2n th root of unity in a Galois extension of Z4, then C is a t Lee error-correcting code. We present a corresponding decoding algorithm that corrects any t Lee errors. The treatment given here uses techniques from Groebner bases, although this is not essential to the decoding method.
Prochains exposés
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Key Attack on the ACDGV Matrix Encryption Scheme
Orateur : Anmoal Porwal - Technical University of Munich
I will present our key-recovery attack on the ACDGV public-key encryption scheme proposed at ASIACRYPT 2024 by Aragon, Couvreur, Dyseryn, Gaborit, and Vinçotte. The secret key is a Gabidulin code hidden by appending random rows and columns and by left- and right-multiplication with invertible matrices. Our attack exploits the resulting algebraic structure to recover an equivalent secret key. It[…]-
Cryptography
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Asymmetric primitive
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Module Learning With Errors and Structured Extrapolated Dihedral Cosets
Orateur : Jinwei Zheng - Télécom Paris
The Module Learning With Errors (MLWE) problem is the fundamental hardness assumption underlying the key encapsulation and signature schemes ML-KEM and ML-DSA, which have been selected by NIST for post-quantum cryptography standardization. Understanding its quantum hardness is crucial for assessing the security of these standardized schemes. Inspired by the equivalence between LWE and[…]-
Cryptography
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