Security of a new digital signature scheme based on factoring and discrete logarithms

Abstract

A new digital signature scheme based on the difficulties of simultaneously solving the factoring and discrete logarithm problems has recently been proposed by Tzeng et al. zeng, S.-F., Yang, C.-Y. and Hwang, M.-S., 2004, A new digital signature scheme based on factorings and discrete logarithms. International Journal of Computer Mathematics, 81, 9–14.). In the proposed scheme, each user uses a common arithmetic modulus and only owns one private key and one public key. Although Tzeng and colleagues claimed that their scheme cannot be overruled by some possible limitations, we show that their scheme is not secure if attackers can solve discrete logarithm problems or factoring composite numbers.

Keywords:

• Cryptography
• Digital signature
• Factoring
• Discrete logarithm

Acknowledgements

This work was supported by Zhejiang Provincial Natural Science Foundation of China under Grant Y104201.