论文信息 - Improving and Extending the Lim/Lee Exponentiation Algorithm

Improving and Extending the Lim/Lee Exponentiation Algorithm

. In [5] Lim and Lee present an algorithm for fast exponentiation in a given group which is optimized for a limited amount of storage. The algorithm uses one precomputation for several computations in order to minimize the average time needed for one exponentiation. This paper generalizes the previous work proposing several improvements and a method for fast precomputation. The basic Lim/Lee algorithm is improved by determining the optimal segmentation of the exponent. Finally, it is shown that the improved Lim/Lee algorithm is faster than the previous one in average case.

[1] C. Mitchell,et al. Minimum weight modified signed-digit representations and fast exponentiation , 1989 .

[2] Ernest F. Brickell,et al. An Interactive Identification Scheme Based on Discrete Logarithms and Factoring , 1990, EUROCRYPT.

[3] Donald E. Knuth,et al. The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .

[4] Donald Ervin Knuth,et al. The Art of Computer Programming , 1968 .

[5] Alfredo De Santis,et al. Advances in Cryptology — EUROCRYPT'94 , 1994, Lecture Notes in Computer Science.

[6] Yvo Desmedt,et al. Advances in Cryptology — CRYPTO ’94 , 2001, Lecture Notes in Computer Science.

[7] Peter de Rooij,et al. Efficient Exponentiation using Procomputation and Vector Addition Chains , 1994, EUROCRYPT.

[8] Alfred Menezes,et al. Handbook of Applied Cryptography , 2018 .

[9] Chae Hoon Lim,et al. More Flexible Exponentiation with Precomputation , 1994, CRYPTO.

[10] Matthijs J. Coster,et al. Addition Chain Heuristics , 1989, CRYPTO.

[11] Michael Wiener,et al. Advances in Cryptology — CRYPTO’ 99 , 1999 .

[12] Adi Shamir,et al. A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[13] Donald E. Knuth,et al. The Art of Computer Programming, Vol. 2 , 1981 .