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Register a new userOn Decoding Schemes for the MDPC-McEliece Cryptosystem
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Added by
Hannes Bartz
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Recently, it has been shown how McEliece public-key cryptosystems based on moderate-density parity-check (MDPC) codes allow for very compact keys compared to variants based on other code families. In this paper, classical (iterative) decoding schemes for MPDC codes are considered. The algorithms are analyzed with respect to their error-correction capability as well as their resilience against a recently proposed reaction-based key-recovery attack on a variant of the MDPC-McEliece cryptosystem by Guo, Johansson and Stankovski (GJS). New message-passing decoding algorithms are presented and analyzed. Two proposed decoding algorithms have an improved error-correction performance compared to existing hard-decision decoding schemes and are resilient against the GJS reaction-based attack for an appropriate choice of the algorithms parameters. Finally, a modified belief propagation decoding algorithm that is resilient against the GJS reaction-based attack is presented.
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Two variations of the McEliece cryptosystem are presented. The first one is based on a relaxation of the column permutation in the classical McEliece scrambling process. This is done in such a way that the Hamming weight of the error, added in the encryption process, can be controlled so that efficient decryption remains possible. The second variation is based on the use of spatially coupled moderate-density parity-check codes as secret codes. These codes are known for their excellent error-correction performance and allow for a relatively low key size in the cryptosystem. For both variants the security with respect to known attacks is discussed.
In this paper, ensembles of quasi-cyclic moderate-density parity-check (MDPC) codes based on protographs are introduced and analyzed in the context of a McEliece-like cryptosystem. The proposed ensembles significantly improve the error correction capability of the regular MDPC code ensembles that are currently considered for post-quantum cryptosystems without increasing the public key size. The proposed ensembles are analyzed in the asymptotic setting via density evolution, both under the sum-product algorithm and a low-complexity (error-and-erasure) message passing algorithm. The asymptotic analysis is complemented at finite block lengths by Monte Carlo simulations. The enhanced error correction capability remarkably improves the scheme robustness with respect to (known) decoding attacks.
We illustrate through example 1 and 2 that the condition at theorem 1 in [8] dissatisfies necessity, and the converse proposition of fact 1.1 in [8] does not hold, namely the condition Z/M - L/Ak < 1/(2 Ak^2) is not sufficient for f(i) + f(j) = f(k). Illuminate through an analysis and ex.3 that there is a logic error during deduction of fact 1.2, which causes each of fact 1.2, 1.3, 4 to be invalid. Demonstrate through ex.4 and 5 that each or the combination of qu+1 > qu * D at fact 4 and table 1 at fact 2.2 is not sufficient for f(i) + f(j) = f(k), property 1, 2, 3, 4, 5 each are invalid, and alg.1 based on fact 4 and alg.2 based on table 1 are disordered and wrong logically. Further, manifest through a repeated experiment and ex.5 that the data at table 2 is falsified, and the example in [8] is woven elaborately. We explain why Cx = Ax * W^f(x) (% M) is changed to Cx = (Ax * W^f(x))^d (% M) in REESSE1+ v2.1. To the signature fraud, we point out that [8] misunderstands the existence of T^-1 and Q^-1 % (M-1), and forging of Q can be easily avoided through moving H. Therefore, the conclusion of [8] that REESSE1+ is not secure at all (which connotes that [8] can extract a related private key from any public key in REESSE1+) is fully incorrect, and as long as the parameter Omega is fitly selected, REESSE1+ with Cx = Ax * W^f(x) (% M) is secure.
In this paper we present a new class of convolutional codes that admits an efficient al- gebraic decoding algorithm. We study some of its properties and show that it can decode interesting sequences of errors patterns. The second part of the paper is devoted to in- vestigate its use in a variant of the McEliece cryptosystem. In contrast to the classical McEliece cryptosystems, where block codes are used, we propose the use of a convolu- tional encoder to be part of the public key. In this setting the message is a sequence of messages instead of a single block message and the errors are added randomly throughout the sequence. We conclude the paper providing some comments on the security. Although there is no obvious security threats to this new scheme, we point out several possible adaptations of existing attacks and discuss the difficulties of such attacks to succeed in breaking this cryptosystem.
This article addresses code-based cryptography and is designed to depict the complete outline of a code based public key cryptosystem. This report includes basic mathematics and fundamentals of coding theory which are useful for studying code-based cryptography. Here, we briefly describe the first scheme of code based public key cryptosystems given by R. J. McEliece in 1978 and its improved version given by H. Niederreiter in 1986. We discuss the hard problems of coding theory which are used in code based cryptography and some classic attacks on it like information-set decoding (ISD). Successful implementation of the ISD attack on McEliece cryptosystem for some small parameters set is executed and the code for the same is provided in the Appendix. This report elaborates a key encapsulation mechanism (KEM), namely Classic McEliece, based on algebraic coding theory to establish a symmetric key for two users.
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