30 research outputs found
Flow Secure Message in Parity Matrix
The goal of security is confidential ,integrity and availability to decrypt the messages.In recent years,many researchers has said about how to secure high-value data on hard disk.proposed system explains about the high grade cryptosystem one which even an attacker possessing both a copy of your encryption engine and knowledge of your operation.
DOI: 10.17762/ijritcc2321-8169.15014
Key Reduction of McEliece's Cryptosystem Using List Decoding
International audienceDifferent variants of the code-based McEliece cryptosystem were pro- posed to reduce the size of the public key. All these variants use very structured codes, which open the door to new attacks exploiting the underlying structure. In this paper, we show that the dyadic variant can be designed to resist all known attacks. In light of a new study on list decoding algorithms for binary Goppa codes, we explain how to increase the security level for given public keysizes. Using the state-of-the-art list decoding algorithm instead of unique decoding, we exhibit a keysize gain of about 4% for the standard McEliece cryptosystem and up to 21% for the adjusted dyadic variant
List-Decoding of Binary Goppa Codes up to the Binary Johnson Bound
International audienceWe study the list-decoding problem of alternant codes (which includes obviously that of classical Goppa codes). The major consideration here is to take into account the (small) size of the alphabet. This amounts to comparing the generic Johnson bound to the q-ary Johnson bound. The most favourable case is q = 2, for which the decoding radius is greatly improved. Even though the announced result, which is the list-decoding radius of binary Goppa codes, is new, we acknowledge that it can be made up from separate previous sources, which may be a little bit unknown, and where the binary Goppa codes has apparently not been thought at. Only D. J. Bernstein has treated the case of binary Goppa codes in a preprint. References are given in the introduction. We propose an autonomous and simplified treatment and also a complexity analysis of the studied algorithm, which is quadratic in the blocklength n, when decoding away of the relative maximum decoding radius
The decoding failure probability of MDPC codes
Moderate Density Parity Check (MDPC) codes are defined here as codes which
have a parity-check matrix whose row weight is where is the
length of the code. They can be decoded like LDPC codes but they decode
much less errors than LDPC codes: the number of errors they can decode in this
case is of order . Despite this fact they have been proved
very useful in cryptography for devising key exchange mechanisms. They have
also been proposed in McEliece type cryptosystems. However in this case, the
parameters that have been proposed in \cite{MTSB13} were broken in
\cite{GJS16}. This attack exploits the fact that the decoding failure
probability is non-negligible. We show here that this attack can be thwarted by
choosing the parameters in a more conservative way. We first show that such
codes can decode with a simple bit-flipping decoder any pattern of
errors. This avoids the
previous attack at the cost of significantly increasing the key size of the
scheme. We then show that under a very reasonable assumption the decoding
failure probability decays almost exponentially with the codelength with just
two iterations of bit-flipping. With an additional assumption it has even been
proved that it decays exponentially with an unbounded number of iterations and
we show that in this case the increase of the key size which is required for
resisting to the attack of \cite{GJS16} is only moderate
Multi-Trial Guruswami–Sudan Decoding for Generalised Reed–Solomon Codes
An iterated refinement procedure for the Guruswami--Sudan list decoding
algorithm for Generalised Reed--Solomon codes based on Alekhnovich's module
minimisation is proposed. The method is parametrisable and allows variants of
the usual list decoding approach. In particular, finding the list of
\emph{closest} codewords within an intermediate radius can be performed with
improved average-case complexity while retaining the worst-case complexity.Comment: WCC 2013 International Workshop on Coding and Cryptography (2013
Flexible Quasi-Dyadic Code-Based Public-Key Encryption and Signature
Drawback of code-based public-key cryptosystems is that their public-key size is lage. It takes some hundreds KB to some MB for typical parameters.
While several attempts have been conducted to reduce it,
most of them have failed except one, which is Quasi-Dyadic (QD) public-key (for large extention degrees).
While an attack has been proposed on QD public-key (for small extension degrees), it can be prevented by making the extension degree larger, specifically by making large enough where is the base filed and for a binary code, .
The drawback of QD is, however, it must hold (at least ) where and are the code lenght and the error correction capability of the underlying code.
If it is not satisfied, its key generation fails since it is performed by trial and error.
This condition also prevents QD from generating parameters for code-based digital signatures since without making close to ,
cannot be small.
To overcome these problems, we propose ``Flexible\u27\u27 Quasi-Dyadic (FQD) public-key that can even achieve with one shot.
Advantages of FQD include
1) it can reduce the publi-key size further,
2) it can be applied to code-based digital signatures, too