Abstract
We study the notion of meta-proofs, which, as the name indicates, are proofs about proofs. We employ the notion of meta-proofs to produce a highly efficient oblivous proof of correct exponentiation. It is minimum-knowledge independently of whether the input is valid or not, a property that does not hold for many other protocols (that are zero-knowledge only for valid inputs.) This has direct security implications to multiparty protocols, where the protocols we demonstrate — one interactive and one non-interactive — can be employed to obtain protocol robustness at a low cost. As a result of potential independent interest, we show how to turn any standard discrete log signature scheme into a scheme for proving equality of discrete logarithms. We demonstrate our method using the Schnorr signature scheme.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
M. Bellare, J. Garay, T. Rabin, “Fast Batch Verification for modular Exponentiation and digital Signatures,” Eurocrypt 98, pp. 236–250.
M. Bellare and P. Rogaway, “Random Oracles are Practical: a Paradigms for Designing Efficient Protocols,” Proc. of the 1st ACM Conference on Computer Communication Security, pp. 62–73, 1993.
R. Canetti, O. Goldreich and S. Halevi, “The Random Oracle Methodology, Revisited,” Proc. STOC’98, ACM Press, pp. 209–218, 1998.
D. Chaum, “Blind Signatures for Untraceable Payments,” Advances in Cryptology - Proceedings of Crypto ‘82, pp. 199–203.
D. Chaum, H. Van Antwerpen, “Undeniable Signatures,” Advances in Cryptology - Proceedings of Crypto ‘89, pp. 212–216.
D. Chaum, “Zero-Knowledge Undeniable Signatures,” Eurocrypt ‘80, pp. 458–464.
A. De Santis, Y. Desmedt, Y. Frankel, and M. Yung, “How to Share a Function Securely,” STOC ‘84, pp. 522–533.
T. ElGamal “A Public-Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms,” Crypto ‘84, pp. 10–18.
A. Fujioka, T. Okamoto, K. Ohta, “Interactive Bi-Proof Systems and Undeniable Signature Schemes,” Eurocrypt ‘81, pp. 243–256.
M. Jakobsson, M. Yung, “Proving Without Knowing: On Oblivious, Agnostic and Blindfolded Provers,” Crypto ‘86, pp. 186–200.
M. Jakobsson, K. Sako, R. Impagliazzo, “Designated Verifier Proofs and Their Applications,” Eurocrypt ‘86, pp. 143–154.
National Institute for Standards and Technology, “Digital Signature Standard (DSS),” Federal Register Vol 56(169), Aug 30, 1991.
T.P. Pedersen, “Distributed Provers with Applications to Undeniable Signatures,” Advances in Cryptology - Proceedings of Eurocrypt ‘81, pp. 221–242.
D. Pointcheval and J. Stern, “Security Proofs for Signature Schemes,” Proc. Eurocrypt’96, LNCS 1070, Springer-Verlag, pp. 387–398, 1996.
D. Pointcheval and J. Stern, “Provably Secure Blind Signature Schemes,” Proc. Asiacrypt’96, LNCS 1163, Springer Verlag, pp. 387–393, 1996.
D. Pointcheval, “Strengthened Security for Blind Signatures,” Proc. Eurocrypt’98 LNCS 1403, Springer Verlag, pp. 391–405, 1998.
C.P. Schnorr, “Efficient Signature Generation for Smart Cards,” Advances of Cryptology, Proceedings of Crypto ‘88, pp.239–252.
A. Shamir, “How to Share a Secret,” Communications of the ACM, Vol. 22, 1979, pp. 612–613.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Jakobsson, M., Schnorr, C.P. (1999). Efficient Oblivious Proofs of Correct Exponentiation. In: Preneel, B. (eds) Secure Information Networks. IFIP — The International Federation for Information Processing, vol 23. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35568-9_5
Download citation
DOI: https://doi.org/10.1007/978-0-387-35568-9_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-6487-1
Online ISBN: 978-0-387-35568-9
eBook Packages: Springer Book Archive