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Paper: Fast Digital Signature Schemes as Secure as Diffie-Hellman Assumptions

Authors:
Changshe Ma
Jian Weng
Dong Zheng
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URL: http://eprint.iacr.org/2007/019
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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.
BibTeX
@misc{eprint-2007-13301,
  title={Fast Digital Signature Schemes as Secure as Diffie-Hellman Assumptions},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Public-key cryptography, signature schemes,  discrete logarithm problem, Diffie-Hellman problem, tight reduction},
  url={http://eprint.iacr.org/2007/019},
  note={ changshema@gmail.com 13535 received 22 Jan 2007, last revised 22 Jan 2007},
  author={Changshe Ma and Jian Weng and Dong Zheng},
  year=2007
}