Secured Digital Signature Scheme using Polynomials over Non-Commutative Division Semirings

Digital signatures are probably the most important and widely used cryptographic primitive enabled by public key technology, and they are building blocks of many modern distributed computer applications, like, electronic contract signing, certified email, and secure web browsing etc. But many existing signatures schemes lie in the intractability of problems closely related to the number theory than group theory. In this paper, we propose a new signature scheme based on general non-commutative division semiring. The key idea of our scheme is that for a given non-commutative division semiring, we can build polynomials on additive structure and take them as the underlying work structure. By doing so, we can implement a new signature scheme on multiplicative structure of the semiring. The security of the proposed signature scheme is based on the intractability of the Polynomial Symmetrical Decomposition Problem over the given non-commutative division semiring.