International Association
for Cryptologic Research

In this paper, we propose a new signature scheme connecting two private keys and two public keys based on general non-commutative division semiring. The key idea of our technique engrosses three core steps. In the first step, we assemble polynomials on additive structure of non-commutative division semiring and take them as underlying work infrastructure. In the second step, we generate first set of private and public key pair using polynomial symmetrical decomposition problem. In the third step, we generate second set of private and public key pair using discrete logarithm. We use factorization theorem to generate the private key in discrete logarithm problem. By doing so, we can execute a new signature scheme on multiplicative structure of the semiring using multiple private keys. The security of the proposed signature scheme is based on the intractability of the Polynomial Symmetrical Decomposition Problem and discrete logarithm problem over the given non-commutative division semiring. Hence, this signature scheme is so much strong in security point of view.