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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Algorithms for post-quantum commutative group actions
Orateur : Marc Houben - Inria Bordeaux
At the historical foundation of isogeny-based cryptography lies a scheme known as CRS; a key exchange protocol based on class group actions on elliptic curves. Along with more efficient variants, such as CSIDH, this framework has emerged as a powerful building block for the construction of advanced post-quantum cryptographic primitives. Unfortunately, all protocols in this line of work are[…] -
Endomorphisms via Splittings
Orateur : Min-Yi Shen - No Affiliation
One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. In this talk, we show that the problem is related to the problem of finding a splitting of a principally polarised superspecial abelian surface. In particular, we provide formal security reductions and a proof-of-concept[…]-
Cryptography
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