A fast signature scheme based on congruential polynomial operations

A novel digital signature scheme is proposed in which the computation time is much shorter than that of the Rivest-Shamir-Adelman (RSA) scheme, while the key length and signature length are comparable to those for the RSA scheme. Moreover, the proposed scheme can be implemented easily and is, therefore, more practical for many digital signature applications. The scheme is based on congruential polynomial operations whose degrees are more than three. The secret key consists of two large prime numbers, p and q, and the public key is their product, n=p²q. The security of this scheme depends on the difficulty of factorizing the number n. Variations using the number of zeros succeeding the significant bit are also proposed