The integrated interleaving error correcting scheme is a coding scheme for combining codes with different error correcting capabilities. This method is applied to channels in which a data sequence isâ€¦ (More)

The joint sparse form (JSF) is a representation of a pair of integers, which is famous for accelerating a multi-scalar multiplication in elliptic curve cryptosystems. Solinasâ€™ original paper showedâ€¦ (More)

Several methods for finding a basis conversion matrix between two different bases in an extension field have been proposed. Among them, the one based on Gauss period normal basis (GNB) is on averageâ€¦ (More)

We have shown that the coding scheme can be applied to codes with a sum-product(SP) decoding algorithm \cite{kamabekatouMag}. We suppose that we use two different codes, $C_{1}$ and SC_{2}$, withâ€¦ (More)

A square root (SQRT) algorithm in GF (p) (m=r0r1 Â· Â· Â· rnâˆ’12, ri: odd prime, d>0: integer) is proposed in this paper. First, the TonelliShanks algorithm is modified to compute the inverse SQRT in GFâ€¦ (More)

2009 Fourth International Conference on Computerâ€¦

2009

This paper shows two improvements of twisted-Ate pairing with Barreto-Naehrig curve so as to be efficiently carried out by dividing the calculation loops of Miller's algorithm based on divisorâ€¦ (More)