Omessaad Hamdi

Hidden Field Equations Cryptosystem Performances

It is pointed out in (1) that HFE is faster than RSA, but it has larger key storage. In this paper, we will outline some of its advantages and disadvantages. We will also study the fact of the extension field degree and the private key degree on the speed of key generation, encryption and decryption.

Performance of LDPC Decoding Algorithms with a Statistical Physics Theory Approach

In 1989, N.Sourlas used the parallel that exists between the information theory and the statistical physics to bring out that low density parity check (LDPC) codes correspond to spins glass models. Such a correspondence is contributing nowadays to the similarity between the statistical physics and the error correcting codes. Hence, the statistical physics methods have been applied to study the properties of these codes. Among these methods the Thouless-Anderson-Palmer (TAP) is an approach which is proved to be similar to the Belief Propagation (BP) algorithm. Unfortunately, there are no studies made for the other decoding algorithms.

Magnetization performance of BP-Based algorithm

In this paper, we present the performance of the Belief Propagation-Based (BP-Based) algorithm as a function of the magnetization. Previous works, have shown that the BP algorithm, is equivalent to the Thouless- Anderson-Palmer(TAP) [1] approach, we develop the log-likelihood ratios-Belief Propagation (LLR-BP) algorithm and its simplification, the BP-Based algorithm using this method.

Weakness on Cryptographic Schemes Based on Chained Codes

We propose a method to recover the structure of a randomly permuted chained code and how to cryptanalyse cryptographic schemes based on these kinds of error coding. This result prohibits the use of chained code on cryptography.

Iterative decoding algorithms of LDPC codes using TAP approach

Low-density parity-check (LDPC) codes are based on random construction. Because of this randomness, it is not easy to analyze them with the traditional methods of communication theory. N.Sourlas [6] was the first to point out that LDPC codes have a similarity to Ising spin systems in statistical physics. Besides, it has been shown that the Belief-Propagation algorithm, the decoding algorithm of LDPC codes, is equivalent to the Thouless-Anderson-Palmer(TAP) [9] approach. In this paper, we develop the log-likelihood ratios-Belief Propagation (LLR-BP) and the BP-Based decoding algorithms with the TAP approach.