Code-Based Cryptosystems Using Generalized Concatenated Codes

Puchinger, Sven; Müelich, Sven; Ishak, Karim; Bossert, Martin

doi:10.1007/978-3-319-56932-1_26

Cited by 6 publications

(8 citation statements)

References 22 publications

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“…Goppa codes are still considered to be secure, as no structural attacks on these codes were found. On the other hand, the proposed GC code construction has no complete security analysis against structural attacks, such as the attacks proposed in [21,26,33]. This security analysis is subject to future work.…”

Section: Discussionmentioning

confidence: 99%

“…In [26], it was shown that generalized concatenated codes may withstand the aforementioned structural attacks. Furthermore, those codes enable higher code rates.…”

Section: Generalized Concatenated (Gc) Codes Over Gaussian and Eisens...mentioning

confidence: 99%

“…In this work, we propose a new code construction based on generalized concatenated (GC) codes. This construction is motivated by the results in [26], which show that GC codes are more robust against structural attacks than ordinary concatenated codes. Furthermore, we adapt the code construction to Eisenstein integers.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography

Thiers

Freudenberger

2021

Cryptography

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The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem, together with the one-Mannheim error channel, where the error values are limited to the Mannheim weight one. Due to the limited error values, the codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This higher error correction capability improves the work factor regarding decoding attacks based on information-set decoding. The codes also enable a low complexity decoding algorithm for decoding beyond the guaranteed error correction capability. In this work, we extend this coding scheme to codes over Eisenstein integers. These codes have advantages for the Niederreiter system. Additionally, we propose an improved code construction based on generalized concatenated codes. These codes extend to the rate region, where the work factor is beneficial compared to MDS codes. Moreover, generalized concatenated codes are more robust against structural attacks than ordinary concatenated codes.

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Section: Discussionmentioning

confidence: 99%

“…In [26], it was shown that generalized concatenated codes may withstand the aforementioned structural attacks. Furthermore, those codes enable higher code rates.…”

Section: Generalized Concatenated (Gc) Codes Over Gaussian and Eisens...mentioning

confidence: 99%

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Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography

Thiers

Freudenberger

2021

Cryptography

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“…Interleaved Goppa [94] GRS Ordinary concatenated [197] [198] Generalized concatenated [182] Table 18: Proposals for the McEliece Framework…”

Section: Code Proposed In Attackmentioning

confidence: 99%

A Survey on Code-Based Cryptography

Weger¹,

Gassner²,

Rosenthal³

2022

Preprint

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The improvements on quantum technology are threatening our daily cybersecurity, as a capable quantum computer can break all currently employed asymmetric cryptosystems. In preparation for the quantum-era the National Institute of Standards and Technology (NIST) has initiated a standardization process for public-key encryption (PKE) schemes, key-encapsulation mechanisms (KEM) and digital signature schemes. With this chapter we aim at providing a survey on code-based cryptography, focusing on PKEs and signature schemes. We cover the main frameworks introduced in code-based cryptography and analyze their security assumptions. We provide the mathematical background in a lecture notes style, with the intention of reaching a wider audience.

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“…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%

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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Code-Based Cryptosystems Using Generalized Concatenated Codes

Cited by 6 publications

References 22 publications

Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography

Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography

A Survey on Code-Based Cryptography

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

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