Code-Based Cryptography With Generalized Concatenated Codes for Restricted Error Values

Abstract

Code-based cryptosystems are promising candidates for post-quantum cryptography. Recently, generalized concatenated codes over Gaussian and Eisenstein integers were proposed for those systems. For a channel model with errors of restricted weight, those q-ary codes lead to high error correction capabilities. Hence, these codes achieve high work factors for information set decoding attacks. In this work, we adapt this concept to codes for the weight-one error channel, i.e., a binary channel model where at most one bit-error occurs in each block of m bits. We also propose a low complexity decoding algorithm for the proposed codes. Compared to codes over Gaussian and Eisenstein integers, these codes achieve higher minimum Hamming distances for the dual codes of the inner component codes. This property increases the work factor for a structural attack on concatenated codes leading to higher overall security. For comparable security, the key size for the proposed code construction is significantly smaller than for the classic McEliece scheme based on Goppa codes. INDEX TERMS Code-based cryptography, generalized concatenated codes, McEliece cryptosystem, public-key cryptography, restricted error values.

Novel q-ary Code Design for One Edit or Adjacent Transposition Error

“…Then, the error values for Da and Ib scenarios are identified by (5). The difference between c and ĉ in Sĉ is given by (5), and the difference between d 2 and d 1 in Td 2 d 1 is determined by (6). Finally, based on the information about the error values, the constraint (7) produces the error positions and corrects the codewords.…”

“…In spite of many challenges of involved correction code designs [5], [6], a lot of efforts have focused on designing efficient and robust approaches to cope with a single deletion, or insertion error (known as an indel error), a single deletion, insertion, or substitution error (called an edit error), or adjacent transposition error. For instance, in 1965, a binary Varshamov-Tenengolts (VT) code [7] was first presented to correct a single indel error.…”

“…This has the potential to significantly enhance the efficiency of information synchronization in communication systems or the retrieval process in storage systems. Such codes can give rise to numerous applications in synchronizing information across communication and storage contexts [6], [13], [14].…”