Masakatu Morii

Generalized key-equation of remainder decoding algorithm for Reed-Solomon codes

A key equation of the remainder decoding algorithm is presented. It is noted that the key equation presents a general relationship between the errors on the received codeword and the coefficients of the remainder polynomial. It is shown that several key equations proposed by L. Welch and E.R. Berlekamp (1983) and others can be derived from the proposed key equation. Useful properties of the key equations in fast decoding of Reed-Solomon codes are given. >

Perfect staircase profile of linear complexity for finite sequences

Abstract One of the most interesting themes in cryptology is the generating of the highly unpredictable pseudo-random sequences. Unfortunately, it is difficult even to define what the highly unpredictable pseudo-random sequences are. However, some measures for the unpredictability, or equivalently the randomness, of finite sequences were proposed. The linear complexity is one of such measures. We present new classes of sequences with the interesting growth property of linear complexity.

Exponetiation in Finite Fields Using Dual Basis Multiplier

Implementing finite fields arithmetic is very important, when realizing error control systems and cryptosystems. Recenty several algorithms for implementing multiplication in GF(2 m ) have been proposed. When using the polynomial (or standard) basis representation, it is also important that efficient squaring algorithm is improved.

A note on aliasing probability for multiple input signature analyzer

Recently D.K. Pradhan, S.K. Gupta and M.G. Karpovsky (1990) affirmed that the codes generated by (x- alpha )(x- beta ) were not Reed-Solomon, where alpha and beta were roots of the distinct primitive polynomials of degree m. It was assumed that beta = alpha /sup 8/, where s-1 and 2/sup m/-1 were mutually prime. The authors show that under the above assumption the respective codes are Reed-Solomon codes. >

Some Linear Complexity Profiles of Finite Sequences

One of the most them interesting them in modern crytology is the generating of the highly unpredictable pseudo-random sequences. It is difficult that we give the practical definition of the highly unpredictable pseudo-random sequences. However some measures for the unpredictability, or equivalently the randomness, of finite sequences have been proposed. The linear complexity is one of such measures.In this paper we shall give the notes on the growth properties of linear complexity. Especially we shall present and discuss new classes of sequences with the interesting growth property of linear complexity.