## FACTOR-4 AND 6 COMPRESSION OF CYCLOTOMIC Subgroups Of . . . (2009)

Citations: | 3 - 3 self |

### BibTeX

@MISC{Karabina09factor-4and,

author = {Koray Karabina},

title = {FACTOR-4 AND 6 COMPRESSION OF CYCLOTOMIC Subgroups Of . . . },

year = {2009}

}

### OpenURL

### Abstract

Bilinear pairings derived from supersingular elliptic curves of embedding degrees 4 and 6 over finite fields F2 m and F3m, 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 22m + 1 and 32m − 3m + 1, respectively, of the multiplicative groups F ∗ 24m and F ∗ 36m. 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.