Left-to-right binary signed-digit recoding for elliptic curve cryptography

In this paper we present a new left-to-right (i.e., from the most significant bit to the least significant bit) algorithm to compute the binary signed-digit representations of two integers g and h such that their joint weight is optimal. This method has lower complexity compared to the best known method JSF (Joint Sparse Form) algorithm. This method can be easily extended to the case of finding the signed-digit representation of more than two integers. In [1] Solinas left this as an open problem. Such an algorithm is useful in simplifying the circuits for the implementation of elliptic curve cryptosystems (ECC).