A Decoder for a Lightweight McEliece Cryptosystem Based on Concatenated Codes

Thiers, Johann-Philipp; Freudenberger, Jürgen

doi:10.1109/mce.2022.3192126

Cited by 1 publication

(3 citation statements)

References 16 publications

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“…In [34], an FPGA implementation of a GC decoder is presented and compared to hardware decoders for binary Goppa codes as well as QC-MDPC codes. This implementation shows, that the proposed GC codes allow for a very efficient decoding, which significantly reduces the area and time requirements in comparison to the decoder for Goppa codes.…”

Section: Discussionmentioning

confidence: 99%

“…The QC-MDPC-based systems have significantly higher decoding complexity. This was shown in [34], where an FPGA implementation of the proposed decoding method was presented. A comparison to the QC-MDPC decoder from [23] showed that the proposed GC decoder is three times faster and requires less than 1% of the logic of the QC-MDPC decoder for the same security category.…”

Section: Comparison With Other Code-based Cryptosystemsmentioning

confidence: 94%

“…We compare the proposed coding scheme with other proposals for the McEliece system [30], [31], [32] in terms of their public key sizes for the same security category in the current NIST standardization process [33]. It is shown in [34] that the GC codes also have advantages concerning the size and speed of hardware implementations of the decoder.…”

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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Section: Discussionmentioning

confidence: 99%

Section: Comparison With Other Code-based Cryptosystemsmentioning

confidence: 94%