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Journal of Cryptology

, Volume 28, Issue 1, pp 176–208 | Cite as

Confined Guessing: New Signatures From Standard Assumptions

  • Florian Böhl
  • Dennis Hofheinz
  • Tibor JagerEmail author
  • Jessica Koch
  • Christoph Striecks
Article

Abstract

We put forward a new technique to construct very efficient and compact signature schemes. Our technique combines several instances of only a mildly secure signature scheme to obtain a fully secure scheme. Since the mild security notion we require is much easier to achieve than full security, we can combine our strategy with existing techniques to obtain a number of interesting new (stateless and fully secure) signature schemes. Concretely, we get (1) A scheme based on the computational Diffie–Hellman (CDH) assumption in pairing-friendly groups. Signatures contain \(\mathbf {O}(1)\) and verification keys \(\mathbf {O}(\log k)\) group elements, where \(k\) is the security parameter. Our scheme is the first fully secure CDH-based scheme with such compact verification keys. (2) A scheme based on the (nonstrong) RSA assumption in which both signatures and verification keys contain \(\mathbf {O}(1)\) group elements. Our scheme is significantly more efficient than existing RSA-based schemes. (3) A scheme based on the Short Integer Solutions (SIS) assumption. Signatures contain \(\mathbf {O}(\log (k)\cdot m)\) and verification keys \(\mathbf {O}(n\cdot m) {\mathbb {Z}}_p\)-elements, where \(p\) may be polynomial in \(k\), and \(n,m\) denote the usual SIS matrix dimensions. Compared to state-of-the-art SIS-based schemes, this gives very small verification keys, at the price of slightly larger signatures. In all cases, the involved constants are small, and the arising schemes provide significant improvements upon state-of-the-art schemes. The only price we pay is a rather large (polynomial) loss in the security reduction. However, this loss can be significantly reduced at the cost of an additive term in signature and verification key size.

Keywords

Digital signatures CDH assumption Pairing-friendly groups  RSA assumption SIS assumption 

Notes

Acknowledgments

The authors thank Ronald Cramer for his helpful comments, in particular on the presentation of our results, and the anonymous referees for providing valuable feedback.

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Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Florian Böhl
    • 1
  • Dennis Hofheinz
    • 1
  • Tibor Jager
    • 2
    Email author
  • Jessica Koch
    • 1
  • Christoph Striecks
    • 1
  1. 1.Karlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Ruhr-Universität BochumBochumGermany

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