DESIGN OF A DIGITAL SIGNATURE SCHEME BASED ON FACTORING AND DISCRETE LOGARITHMS

摘要

Objective Focusing on the security problem of authentication and confidentiality in the context of computer networks, a digital signature scheme was proposed based on the public key cryptosystem. Methods Firstly, the course of digital signature based on the public key cryptosystem was given. Then, RSA and ELGamal schemes were described respectively. They were the basis of the proposed scheme. Generalized ELGamal type signature schemes were listed. After comparing with each other, one scheme, whose Signature equation was (m+r)x = j + s mod"I>(p) , was adopted in the designing. Results Based on two well-known cryptographic assumptions, the factorization and the discrete logarithms, a digital signature scheme was presented. It must be required that s' was not equal to p' q' in the signing procedure, because attackers could forge the signatures with high probabilities if the discrete logarithms modulo a large prime were solvable. The variable public key "e" is used instead of the invariable parameter "3" in Harn's signature scheme to enhance the security. One generalized ELGamal type scheme made the proposed scheme escape one multiplicative inverse operation in the signing procedure and one modular exponentiation in the verification procedure. Conclusion The presented scheme obtains the security that Harn's scheme was originally claimed. It is secure if the factorization and the discrete logarithms are simultaneously unsolvable.