Novel Digital Signature Scheme with Multiple Private Keys on Non-commutative Division Semirings

Abstract

In this article, we propose a novel signature scheme connecting two private keys and two public keys generated on general non-commutative division semiring. The key notion of our technique engrosses three core steps. In the first step, we assemble polynomials on additive structure of non-commutative division semiring and execute them as underlying base 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 making so, we can execute a new signature scheme on multiplicative algebraic structure of the semiring using multiple private keys. The security of the designed signature scheme is depending on the intractability or hardness of the polynomial symmetrical decomposition problem and discrete logarithmic problem over the designed non-commutative division semiring. Hacking or tracking private keys should cross two mathematical hard problems. Hence, this signature scheme is much stronger than existing protocols in security point of view.