**Fast Digital Signature Schemes as Secure as Diffie-Hellman Assumptions**

*Changshe Ma, Jian Weng and Dong Zheng*

**Abstract: **This paper presents two fast digital signature schemes based on Diffie-Hellman assumptions. In the random oracle model, the first scheme S1 has a tight security reduction to the computational Diffie-Hellman (CDH) problem; and the second scheme S2 has a tight security reduction to the decisional Diffie-Hellman (DDH) problem.

Comparing with existing signature schemes (whose security is tightly related to CDH problem) like EDL signature schemes, the signature generation of S1 is about 27% faster, and the verification is about 35% faster, if without considering the hash function evaluations. Comparing with existing signature schemes (whose security is tightly related to DDH problem) like KW-DDH signature scheme, the signing of S2 is about 40% faster and the verification is about 35% faster.

The high efficiency of the proposed schemes is attributed to a new protocol EDL_mwz which implements the proof of equality of discrete logarithm. The EDL_mwz protocol outperforms its counterpart, the Chaum and Pedersen protocol, as its computation is about 38% faster and its bandwidth is |G| bits shorter. This new protocol may be of independent interests.

**Category / Keywords: **public-key cryptography / Public-key cryptography, signature schemes, discrete logarithm problem, Diffie-Hellman problem, tight reduction

**Date: **received 22 Jan 2007, last revised 22 Jan 2007

**Contact author: **changshema at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20070126:190317 (All versions of this report)

**Short URL: **ia.cr/2007/019

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