A simple construction of pseudorandom generator is appear.This pseudorandom generator is always passed by NIST statistical test.This paper reports a pseudorandom number generator which has good property is able to construct using only permutation and data rewriting by XOR.

MDS matrices are used as building blocks of diffusion layers in block ciphers, and XOR count is a metric that estimates the hardware implementation cost. In this paper we report the minimum value of XOR counts of 4 × 4 MDS matrices over F24 and F28 , respectively. We give theoretical constructions of Toeplitz MDS matrices and show that they achieve the minimum XOR count. We also prove that Toep...

Maximal distance separable (MDS) matrices are important components for block ciphers. In this paper, we present an algorithm for searching 4 × 4 MDS matrices over GL(4, F2). By this algorithm, we find all the lightest MDS matrices have only 10 XOR counts. Besides, all these lightest MDS matrices are classified to 3 types, and some necessary and sufficient conditions are presented for them as we...

This paper introduces a new approach for implementing GF(2 m ) multiplication using Polynomial Residue Number Systems (PRNS). Irreducible trinomials are selected as the generating polynomials for the PRNS channels to enable conversion to-and-from PRNS to be implemented using simple XOR networks. A novel approach for modular reduction over GF(2 m ) is also presented for the PRNS architecture to ...

In the present paper, we investigate the problem of constructing MDS matrices with as few bit XOR operations as possible. The key contribution of the present paper is constructing MDS matrices with entries in the set of m ×m non-singular matrices over F2 directly, and the linear transformations we used to construct MDS matrices are not assumed pairwise commutative. With this method, it is shown...

The array erasure code, an ideal method for fault tolerance in storage systems, however, is obstructed by its impossibility to set the fault tolerant ability according to dynamic application environment for practical purpose. In view of this, this paper presents a new class of array erasure codes, with the greatest contribution to the array codes which can be obtained according to the preset nu...

Maximal Distance Separable (MDS) matrices are important components for block ciphers. In this paper, we present an algorithm for searching 4×4 MDS matrices over GL(4,F2). By this algorithm, we find that all the lightest MDS matrices have only 10 XOR counts. Besides, all these lightest MDS matrices can be classified to 3 types, and some necessary and sufficient conditions are presented for them ...

were employed to solving classification problem. Functional networks are generalized neural networks, which permit the specification of their initial topology using knowledge about the problem at hand. In this case, and after analyzing the available data and their relations, we systematically discuss a numerical analysis method used for functional network, and apply two functional network model...

Three-level logic is shown to have a potential for reduction of the area over two-level implementations, as well as for a gain in speed over multi-level implementations. Algorithms for finding AND-OR-XOR and AND-OR-AND expressions were developed, however an open problem remained which of the algorithms should be used to find an optimal solution for a given function. In this paper we formulate a...

During the last decade, an active line of research in proof complexity has been into the space complexity of proofs and how space is related to other measures. By now these aspects of resolution are fairly well understood, but many open problems remain for the related but stronger polynomial calculus (PC/PCR) proof system. For instance, the space complexity of many standard “benchmark formulas”...