84 research outputs found
Assessing and countering reaction attacks against post-quantum public-key cryptosystems based on QC-LDPC codes
Code-based public-key cryptosystems based on QC-LDPC and QC-MDPC codes are
promising post-quantum candidates to replace quantum vulnerable classical
alternatives. However, a new type of attacks based on Bob's reactions have
recently been introduced and appear to significantly reduce the length of the
life of any keypair used in these systems. In this paper we estimate the
complexity of all known reaction attacks against QC-LDPC and QC-MDPC code-based
variants of the McEliece cryptosystem. We also show how the structure of the
secret key and, in particular, the secret code rate affect the complexity of
these attacks. It follows from our results that QC-LDPC code-based systems can
indeed withstand reaction attacks, on condition that some specific decoding
algorithms are used and the secret code has a sufficiently high rate.Comment: 21 pages, 2 figures, to be presented at CANS 201
Using LDGM Codes and Sparse Syndromes to Achieve Digital Signatures
In this paper, we address the problem of achieving efficient code-based
digital signatures with small public keys. The solution we propose exploits
sparse syndromes and randomly designed low-density generator matrix codes.
Based on our evaluations, the proposed scheme is able to outperform existing
solutions, permitting to achieve considerable security levels with very small
public keys.Comment: 16 pages. The final publication is available at springerlink.co
Security and complexity of the McEliece cryptosystem based on QC-LDPC codes
In the context of public key cryptography, the McEliece cryptosystem
represents a very smart solution based on the hardness of the decoding problem,
which is believed to be able to resist the advent of quantum computers. Despite
this, the original McEliece cryptosystem, based on Goppa codes, has encountered
limited interest in practical applications, partly because of some constraints
imposed by this very special class of codes. We have recently introduced a
variant of the McEliece cryptosystem including low-density parity-check codes,
that are state-of-the-art codes, now used in many telecommunication standards
and applications. In this paper, we discuss the possible use of a bit-flipping
decoder in this context, which gives a significant advantage in terms of
complexity. We also provide theoretical arguments and practical tools for
estimating the trade-off between security and complexity, in such a way to give
a simple procedure for the system design.Comment: 22 pages, 1 figure. This paper is a preprint of a paper accepted by
IET Information Security and is subject to Institution of Engineering and
Technology Copyright. When the final version is published, the copy of record
will be available at IET Digital Librar
Cryptanalysis of Two McEliece Cryptosystems Based on Quasi-Cyclic Codes
We cryptanalyse here two variants of the McEliece cryptosystem based on
quasi-cyclic codes. Both aim at reducing the key size by restricting the public
and secret generator matrices to be in quasi-cyclic form. The first variant
considers subcodes of a primitive BCH code. We prove that this variant is not
secure by finding and solving a linear system satisfied by the entries of the
secret permutation matrix.
The other variant uses quasi-cyclic low density parity-check codes. This
scheme was devised to be immune against general attacks working for McEliece
type cryptosystems based on low density parity-check codes by choosing in the
McEliece scheme more general one-to-one mappings than permutation matrices. We
suggest here a structural attack exploiting the quasi-cyclic structure of the
code and a certain weakness in the choice of the linear transformations that
hide the generator matrix of the code. Our analysis shows that with high
probability a parity-check matrix of a punctured version of the secret code can
be recovered in cubic time complexity in its length. The complete
reconstruction of the secret parity-check matrix of the quasi-cyclic low
density parity-check codes requires the search of codewords of low weight which
can be done with about operations for the specific parameters
proposed.Comment: Major corrections. This version supersedes previuos one
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