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Making Existential-unforgeable Signatures Strongly Unforgeable in the Quantum Random-oracle Model

Authors Edward Eaton, Fang Song

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Edward Eaton
Fang Song

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Edward Eaton and Fang Song. Making Existential-unforgeable Signatures Strongly Unforgeable in the Quantum Random-oracle Model. In 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 44, pp. 147-162, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.TQC.2015.147

Abstract

Strongly unforgeable signature schemes provide a more stringent security guarantee than the standard existential unforgeability. It requires that not only forging a signature on a new message is hard, it is infeasible as well to produce a new signature on a message for which the adversary has seen valid signatures before. Strongly unforgeable signatures are useful both in practice and as a building block in many cryptographic constructions. This work investigates a generic transformation that compiles any existential-unforgeable scheme into a strongly unforgeable one, which was proposed by Teranishi et al. [Teranishi/Oyama/Ogata, Cryptology-Indocrypt 2006] and was proven in the classical random-oracle model. Our main contribution is showing that the transformation also works against quantum adversaries in the quantum random-oracle model. We develop proof techniques such as adaptively programming a quantum random-oracle in a new setting, which could be of independent interest. Applying the transformation to an existential-unforgeable signature scheme due to Cash et al. [Cash/Hofheinz/Kiltz/Peikert, J. of Cryptology 2012], which can be shown to be quantum-secure assuming certain lattice problems are hard for quantum computers, we get an efficient quantum-secure strongly unforgeable signature scheme in the quantum random-oracle model.
Keywords
  • digital signatures
  • strongly unforgeable
  • quantum random-oracle
  • lattices

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