Factor-4 and 6 compression of cyclotomic subgroups of and

Journal of mathematical cryptology

article

Koray Karabina¹ 

[1] Department of Combinatorics and Optimization, University of Waterloo

关键词: Finite field compression;    cyclotomic subgroups;    pairing-based cryptography;   

DOI  :  10.1515/jmc.2010.001

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

Bilinear pairings derived from supersingular elliptic curves of embedding degrees 4 and 6 over finite fields ? 2 m and ? 3 m , respectively, have been used to implement pairing-based cryptographic protocols. The pairing values lie in certain prime-order subgroups of the cyclotomic subgroups of orders 2 2 m + 1 and 3 2 m – 3 m + 1, respectively, of the multiplicative groups and . It was previously known how to compress the pairing values over characteristic two fields by a factor of 2, and the pairing values over characteristic three fields by a factor of 6. In this paper, we show how the pairing values over characteristic two fields can be compressed by a factor of 4. Moreover, we present and compare several algorithms for performing exponentiation in the prime-order subgroups using the compressed representations. In particular, in the case where the base is fixed, we expect to gain at least a 54% speed up over the fastest previously known exponentiation algorithm that uses factor-6 compressed representations.

【 授权许可】

CC BY|CC BY-NC-ND