Tighter Reductions for Forward-Secure Signature Schemes
In this paper, we revisit the security of factoring-based signature schemes built via the Fiat-Shamir transform and show that they can admit tighter reductions to certain decisional complexity assumptions such as the quadratic-residuosity, the high-residuosity, and the φ-hiding assumptions. We do so by proving that the underlying identification schemes used in these schemes are a particular case of the lossy identification notion recently introduced by Abdalla et al. at Eurocrypt 2012. Next, we show how to extend these results to the forward-security setting based on ideas from the Itkis-Reyzin forward-secure signature scheme. Unlike the original Itkis-Reyzin scheme, our construction can be instantiated under different decisional complexity assumptions and has a much tighter security reduction. Finally, we show that the tighter security reductions provided by our proof methodology can result in concrete efficiency gains in practice, both in the standard and forward-security setting, as long as the use of stronger security assumptions is deemed acceptable. All of our results hold in the random oracle model.
KeywordsSignature Scheme Random Oracle Security Parameter Full Version Random Oracle Model
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- 2.Abdalla, M., Ben Hamouda, F., Pointcheval, D.: Tighter Reductions for Forward-Secure Signature Schemes. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 292–311. Springer, Heidelberg (2013), full version available from the webpage of the authorsGoogle Scholar
- 5.Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 1993, pp. 62–73. ACM Press (November 1993)Google Scholar
- 7.ECRYPT II yearly report on algorithms and keysizes (2011)Google Scholar
- 17.Katz, J., Wang, N.: Efficiency improvements for signature schemes with tight security reductions. In: Jajodia, S., Atluri, V., Jaeger, T. (eds.) ACM CCS 2003, pp. 155–164. ACM Press (October 2003)Google Scholar
- 20.Micali, S.: A secure and efficient digital signature algorithm. Technical Memo MIT/LCS/TM-501b, Massachusetts Institute of Technology, Laboratory for Computer Science (April 1994)Google Scholar
- 22.Micali, S., Reyzin, L.: Improving the exact security of digital signature schemes. Journal of Cryptology 15(1), 1–18 (2002), full version of Google Scholar