On the Modifications of a Digital Signature Algorithm with Secret Sharing

Abstract

Cryptographic algorithms are vulnerable not only from attacks, but also from the issues raising from storing the private key. Once the private key is leaked, no matter how strong the algorithms are claimed to be, we are severely compromised and hence, lose the secrecy. One of the solutions to remedy this situation is to employ the secret sharing scheme. The basic idea of secret sharing is to split one private key value into several share values. Those share values are then stored into different places by different secret shareholders. The presence of only one share value cannot represent the whole secret value, and further, is unable to reconstruct the private key. In this study, we inserted a secret sharing scheme into a digital signature algorithm based on conic curve cryptography. We opted to perform the scheme on conic based algorithm because these curves are believed to have simpler computations than those of elliptic curves. We split the private key value into several share values, which are then utilized to generate signature values. The alteration on the signature value generation process (by adding a secret sharing scheme) does not alter the verification process taking place on the original algorithm (without the secret sharing scheme). We also employed an additional mechanism by using the solution of congruence system based on the Chinese Remainder Theorem (CRT) and Fermat’s Little Theorem. The whole process is expected to provide if not layers of security, a mechanism in which we can mitigate the possibility of losing secrecy.