Optimization of the parity-check matrix density in QC-LDPC code-based McEliece cryptosystems
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This paper proposes a procedure for selecting the density of the private parity-check matrix, based on the security level and the decryption complexity, and provides some examples of the system parameters obtained through the proposed technique.Abstract:
Low-density parity-check (LDPC) codes are one of the most promising families of codes to replace the Goppa codes originally used in the McEliece cryptosystem. In fact, it has been shown that by using quasi-cyclic low-density parity-check (QC-LDPC) codes in this system, drastic reductions in the public key size can be achieved, while maintaining fixed security levels. Recently, some proposals have appeared in the literature using codes with denser parity-check matrices, named moderate-density parity-check (MDPC) codes. However, the density of the parity-check matrices to be used in QC-LDPC code-based variants of the McEliece cryptosystem has never been optimized. This paper aims at filling such gap, by proposing a procedure for selecting the density of the private parity-check matrix, based on the security level and the decryption complexity. We provide some examples of the system parameters obtained through the proposed technique.read more
Citations
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Journal ArticleDOI
Enhanced Public Key Security for the McEliece Cryptosystem
TL;DR: This paper studies a variant of the McEliece cryptosystem able to ensure that the code used as the public key is no longer permutation equivalent to the secret code, thus opening the way for reconsidering the adoption of classical families of codes, like Reed–Solomon codes, that have been longly excluded from the Mceliece Cryptosystem for security reasons.
Book
QC-LDPC Code-Based Cryptography
TL;DR: This book describes the fundamentals of cryptographic primitives based on quasi-cyclic low-density parity-check (QC-LDPC) codes, with a special focus on the use of these codes in public-key cryptosystems derived from the McEliece and Niederreiter schemes.
Journal ArticleDOI
Squaring attacks on McEliece public-key cryptosystems using quasi-cyclic codes of even dimension
Carl Löndahl,Thomas Johansson,Masoumeh Koochak Shooshtari,Mahmoud Ahmadian-Attari,Mohammad Reza Aref +4 more
TL;DR: A general purpose algorithm for finding low-weight codewords as well as for decoding a received codeword in any quasi-cyclic code whose length and dimension is a multiple of a power of 2.
Posted Content
LEDAkem: a post-quantum key encapsulation mechanism based on QC-LDPC codes
TL;DR: In this article, a code-based key encapsulation mechanism (KEM) called LEDAkem is presented, which relies on quasi-cyclic low-density parity-check codes as secret codes, providing high decoding speeds and compact keypairs.
Posted Content
Using LDGM Codes and Sparse Syndromes to Achieve Digital Signatures
TL;DR: The proposed scheme exploits sparse syndromes and randomly designed low-density generator matrix codes to achieve considerable security levels with very small public keys.
References
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Book
Low-Density Parity-Check Codes
TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.
Journal ArticleDOI
Good error-correcting codes based on very sparse matrices
TL;DR: It is proved that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit, and experimental results for binary-symmetric channels and Gaussian channels demonstrate that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved.
Proceedings ArticleDOI
MDPC-McEliece: New McEliece variants from Moderate Density Parity-Check codes
TL;DR: In this paper, the authors proposed two McEliece variants: one from Moderate Density Parity-Check (MDPC) codes and another from quasi-cyclic MDPC codes.
Book ChapterDOI
Decoding random binary linear codes in 2 n /20 : how 1 + 1 = 0 improves information set decoding
TL;DR: The ball collision technique of Bernstein, Lange and Peters was used to reduce the complexity of Stern's information set decoding algorithm to 20.0556n by as mentioned in this paper, and this bound was improved by May, Meurer and Thomae.
Book ChapterDOI
Attacking and Defending the McEliece Cryptosystem
TL;DR: New parameters for the McEliece and Niederreiter cryptosystems achieving standard levels of security against all known attacks are proposed, and the resulting public-key sizes are considerably smaller than previous parameter choices for the same level of security.