ON THE PARAMETERS OF A McELIECE-TYPE CRYPTOSYSTEM ON D-CODES BASED ON BINARY REED — MULLER CODES
Yury V. Kosolapov, E. A. Lelyuk · PRIKLADNAYa DISKRETNAYa MATEMATIKA · 2025
The characteristics of a McEliece-type code cryptosystem on a special sum of tensor products of base codes, called D-code, are investigated. Binary Reed — Muller codes were chosen as the base codes. Previously, conditions were found for these D-codes, under which the corresponding cryptosystem is resistant to known structural attacks based on the Schur — Hadamard product. However, when using a decoder operating within half the code distance, a McEliece-type system on D-codes provides security comparable to the strength of the classical McEliece cryptosystem on Goppa codes, with a significantly larger key size. In this paper, two probabilistic decoders for D-codes are constructed. In the case of using these decoders, parameters of some D-codes have been found that provide comparable resistance to information set decoding type attacks, while having a smaller key size than in the classical system. However, the presence of a non-negligible decoding failure rate currently limits the scope of application of the D-code cryptosystem to ephemeral session key encapsulation mechanisms (IND-CPA KEM).