Generalized Concatenated Codes over Gaussian Integers for the McEliece Cryptosystem

Thiers, Johann-Philipp; Freudenberger, Jürgen

doi:10.1109/icce-berlin53567.2021.9720027

Cited by 3 publications

(4 citation statements)

References 23 publications

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“…In [21], [22], [26], [42], channel models with restricted error weights were proposed for Gaussian and Eisenstein integers to increase the error correction capability and therefore the security against ISD attacks. In this work, we consider a similar approach by restricting the Hamming weight of m adjacent bits to weight one.…”

Section: The Weight-one Error Channelmentioning

confidence: 99%

“…On the other hand, in [25] an attack on concatenated codes was proposed, which together with the attack on GRS codes [13] can retrieve the private parity check matrix. In [26], a generalized concatenated (GC) code construction with inner OMEC codes over Gaussian integers and outer RS codes was proposed for the one-Mannheim error channel. GC codes are more robust against the structural attack from [25] than ordinary concatenated codes [27].…”

Section: Introductionmentioning

confidence: 99%

“…Alternatively, this channel can be interpreted as a memoryless channel, where the input and the output symbols are from the binary extension field F 2 m and the additive error symbols are limited to the field elements of Hamming weight one. This channel model is similar to the channels for Gaussian and Eisenstein integers which use complex-valued isomorphic representations of prime fields F p and the error symbols are the roots of unity [21], [26], [28]. Likewise, restrictions of the Lee weight of the error symbols are considered in [15], [16], [17], [18], [19], [29].…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, we propose a GC code construction for this weight-one error channel. For the outer codes, we propose RS codes as in [26], which allows for a low complexity erasure decoding. The inner codes are binary Bose-Chaudhuri-Hocquenghem (BCH) codes.…”

Section: Introductionmentioning

confidence: 99%

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

Thiers

Freudenberger

2022

IEEE Open J. Commun. Soc.

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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.

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