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Journal of Information Science and Engineering, Vol. 23 No. 1, pp. 285-298 (January 2007)

Improved Shao's Signature Scheme

H. F. Lin, Jenshiuh Liu and C. Y. Chen*
Department of Information Engineering and Computer Science
*Department of Communications
Feng Chia University
Taichung, 407 Taiwan

In 1998, Shao proposed two digital signature schemes and claimed that the security of which is based on the difficulties of computing both integer factorization and discrete logarithm. However, in 1999, Lee demonstrated that Shaos signature schemes can be broken if the factorization problem can be solved. This paper presents an improvement of Shaos signature schemes and shows that it can resist Lees attack. This makes our proposed scheme based on two hard problems. Some possible common attacks are considered. We show that the problem of recovering the signers secret key from his/her public key is equivalent to solve both the discrete logarithm problem and the factorization problem; the problem of forging a valid signature for a message is at least equivalent to solve the discrete logarithm problem or the factorization problem. In addition, our proposed scheme is immune from substitution and homomorphism attacks.

Keywords: digital signature, factorization problem, discrete logarithm problem, double hard problem, quadratic residue

Full Text () Retrieve PDF document (200701_17.pdf)

Received November 18, 2003; revised July 6 & September 19, 2005; accepted October 31, 2005.
Communicated by Tzong-Chen Wu.