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Two-Party ECDSA from Hash Proof Systems and Efficient Instantiations

  • Guilhem CastagnosEmail author
  • Dario CatalanoEmail author
  • Fabien Laguillaumie
  • Federico Savasta
  • Ida Tucker
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11694)

Abstract

ECDSA is a widely adopted digital signature standard. Unfortunately, efficient distributed variants of this primitive are notoriously hard to achieve and known solutions often require expensive zero knowledge proofs to deal with malicious adversaries. For the two party case, Lindell [Lin17] recently managed to get an efficient solution which, to achieve simulation-based security, relies on an interactive, non standard, assumption on Paillier’s cryptosystem. In this paper we generalize Lindell’s solution using hash proof systems. The main advantage of our generic method is that it results in a simulation-based security proof without resorting to non-standard interactive assumptions.

Moving to concrete constructions, we show how to instantiate our framework using class groups of imaginary quadratic fields. Our implementations show that the practical impact of dropping such interactive assumptions is minimal. Indeed, while for 128-bit security our scheme is marginally slower than Lindell’s, for 256-bit security it turns out to be better both in key generation and signing time. Moreover, in terms of communication cost, our implementation significantly reduces both the number of rounds and the transmitted bits without exception.

Notes

Acknowledgements

The authors would like to thank Benoît Libert for fruitful discussions. This work was supported by the Universita’ degli Studi di Catania, “Piano della Ricerca 2016/2018 Linea di intervento 2”, and the French ANR ALAMBIC project (ANR-16-CE39-0006).

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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.Université de Bordeaux, Inria, CNRS, IMB UMR 5251TalenceFrance
  2. 2.Università di CataniaCataniaItaly
  3. 3.Univ Lyon, EnsL, UCBL, CNRS, Inria, LIPLyon Cedex 07France
  4. 4.Scuola Superiore di CataniaCataniaItaly

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