Chien-Hsing WU Chien-Ming WU Ming-Der SHIEH Yin-Tsung HWANG
In this paper, we present the division algorithm (DA) for the computation of b=c/a over GF(2m) in two aspects. First, we derive a new formulation for the discrete-time Wiener-Hopf equation (DTWHE) Ab = c in GF(2) over any basis. Symmetry of the matrix A is observed on some special bases and a three-step procedure is developed to solve the symmetric DTWHE. Secondly, we extend a variant of Stein's binary algorithm and propose a novel iterative division algorithm EB*. Owing to its structural simplicity, this algorithm can be mapped onto a systolic array with high speed and low area complexity.
Sangook MOON Yong Joo LEE Jae Min PARK Byung In MOON Yong Surk LEE
A new approach on designing a finite field multiplier architecture is proposed. The proposed architecture trades reduction in the number of clock cycles with resources. This architecture features high performance, simple structure, scalability and independence on the choice of the finite field, and can be used in high security cryptographic applications such as elliptic curve crypto-systems in large prime Galois Fields (GF(2m)).
A new elliptic curve scalar multiplication algorithm is proposed. The algorithm offers about twice the throughput of some conventional OEF-base algorithms because it combines the Frobenius map with the table reference method based on base-φ expansion. Furthermore, since this algorithm suits conventional computational units such as 16, 32 and 64 bits, its base field Fpm is expected to enhance elliptic curve operation efficiency more than Fq (q is a prime) or F2n.
The concept of a basis matrix is introduced to investigate the trade-off between complexity and storage for multiplication in a finite field. The effect on the storage requirements of using polynomial and normal bases for element representation is also considered.
Eiji OKAMOTO Wayne AITKEN George Robert BLAKLEY
Polynomials are called permutation polynomials if they induce bijective functions. This paper investigates algebraic properties of permutation polynomials over a finite field, especially properties associated with permutation cycles. A permutation polynomial has a simple structure but good randomness properties suitable for applications. The cycle structure of permutations are considered to be related to randomness. We investigate the algebraic structure from the viewpoint of randomness. First we show the relationship between polynomials and permutations using a matrix equation. Then, we give a general form of a permutation polynomial corresponding to a product C1C2
Tsutomu MORIUCHI Kyoki IMAMURA
This paper presents a new method to derive the phase difference between n-tuples of an m-sequence over GF(p) of period pn-1. For the binary m-sequence of the characteristic polynomial f(x)=xn+xd+1 with d=1,2c or n-2c, the explicit formulas of the phase difference from the initial n-tuple are efficiently derived by our method for specific n-tuples such as that consisting of all 1's and that cosisting of one 1 and n-1 0's, although the previously known formula exists only for that consisting of all 1's.
The competing demands of speed and fault tolerance in finite field Fourier transform implementations have been optimally balanced here by using the chord property in finite field.