QC-LDPC Code-Based Cryptography

Abstract

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A new DNA cryptosystem based on AG codes evaluated in gaussian channels

“…On the other hand, four attacks that have been reported for the McEliece cryptosystem in the past twenty six years [3]. When boundaries are computed for small fields there is a small difference, which could indicate four different attacks, but when the simulation are for larger values of the fields such as those required in this paper, the asymptote is the same for the four attacks.…”

“…The McEliece cryptosystem attacks reported by [3] only consider Goppa codes constructed over the Galois fields G F (2 ω ), whereas we propose to use McEliece cryptosystem and Hermitian codes, that is, construct the generator matrix of the code using rational points on a Hermitian curve H e C over G F((2 q ) 2 ), as shown in Sect. 3.…”

“…When boundaries are computed for small fields there is a small difference, which could indicate four different attacks, but when the simulation are for larger values of the fields such as those required in this paper, the asymptote is the same for the four attacks. Then, the last three attacks can be considered as a variation of the first proposed by Lee-Brickell 1988 attack [3].…”

“…The Hermitian codes have the following parameters: the length of a codeword n = (2 q ) 3 , the length of a message 3 2 q +1 [16,20,21,34].…”

“…A survey of attacks against the McEliece cryptosystem is presented in [3] in which different work factors for classical information set decoding attacks are calculated. For example, at Information Set Decoding (ISD) algorithms the work factor (Lee-Brickell attack in [3]) is given by…”