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Register a new userVariations of the McEliece Cryptosystem
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Added by
Beth Malmskog
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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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.
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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.
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.
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.
A fault injection framework for the decryption algorithm of the Niederreiter public-key cryptosystem using binary irreducible Goppa codes and classical decoding techniques is described. In particular, we obtain low-degree polynomial equations in parts of the secret key. For the resulting system of polynomial equations, we present an efficient solving strategy and show how to extend certain solutions to alternative secret keys. We also provide estimates for the expected number of required fault injections, apply the framework to state-of-the-art security levels, and propose countermeasures against this type of fault attack.
We consider the problem of communicating a message $m$ in the presence of a malicious jamming adversary (Calvin), who can erase an arbitrary set of up to $pn$ bits, out of $n$ transmitted bits $(x_1,ldots,x_n)$. The capacity of such a channel when Calvin is exactly causal, i.e. Calvins decision of whether or not to erase bit $x_i$ depends on his observations $(x_1,ldots,x_i)$ was recently characterized to be $1-2p$. In this work we show two (perhaps) surprising phenomena. Firstly, we demonstrate via a novel code construction that if Calvin is delayed by even a single bit, i.e. Calvins decision of whether or not to erase bit $x_i$ depends only on $(x_1,ldots,x_{i-1})$ (and is independent of the current bit $x_i$) then the capacity increases to $1-p$ when the encoder is allowed to be stochastic. Secondly, we show via a novel jamming strategy for Calvin that, in the single-bit-delay setting, if the encoding is deterministic (i.e. the transmitted codeword is a deterministic function of the message $m$) then no rate asymptotically larger than $1-2p$ is possible with vanishing probability of error, hence stochastic encoding (using private randomness at the encoder) is essential to achieve the capacity of $1-p$ against a one-bit-delayed Calvin.
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