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Reports (Research Report) Year : 2017

On the Tightness of Forward-Secure Signature Reductions

Abstract

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 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. Moreover, we also 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. Finally, we investigate the design of forward-secure signature schemes whose security reductions are fully tight.
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Dates and versions

hal-01667150 , version 1 (19-12-2017)

Identifiers

  • HAL Id : hal-01667150 , version 1

Cite

Michel Abdalla, Fabrice Benhamouda, David Pointcheval. On the Tightness of Forward-Secure Signature Reductions. [Research Report] Report 2017/746, IACR Cryptology ePrint Archive. 2017. ⟨hal-01667150⟩
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