Sealing the Leak on Classical NTRU Signatures

Abstract : Initial attempts to obtain lattice based signatures were closely related to reducing a vector modulo the fundamental parallelepiped of a secret basis (like GGH [9], or NTRUSign [12]). This approach leaked some information on the secret, namely the shape of the parallelepiped, which has been exploited on practical attacks [24]. NTRUSign was an extremely efficient scheme, and thus there has been a noticeable interest on developing countermeasures to the attacks, but with little success [6]. In [8] Gentry, Peikert and Vaikuntanathan proposed a randomized version of Babai’s nearest plane algorithm such that the distribution of a reduced vector modulo a secret parallelepiped only depended on the size of the base used. Using this algorithm and generating large, close to uniform, public keys they managed to get provably secure GGH-like lattice-based signatures. Recently, Stehlé and Steinfeld obtained a provably secure scheme very close to NTRUSign [26] (from a theoretical point of view). In this paper we present an alternative approach to seal the leak of NTRUSign. Instead of modifying the lattices and algorithms used, we do a classic leaky NTRUSign signature and hide it with gaussian noise using techniques present in Lyubashevky’s signatures. Our main contributions are thus a set of strong NTRUSign parameters, obtained by taking into account latest known attacks against the scheme, a statistical way to hide the leaky NTRU signature so that this particular instantiation of CVP-based signature scheme becomes zero-knowledge and secure against forgeries, based on the worst-case hardness of the O~(N1.5) -Shortest Independent Vector Problem over NTRU lattices. Finally, we give a set of concrete parameters to gauge the efficiency of the obtained signature scheme.
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Communication dans un congrès
Lecture Notes in Computer Science. 6th International Workshop, PQCrypto 2014, Oct 2014, Waterloo, Canada. springer, 8772, pp.1-21, 2014, Post-Quantum Cryptography. 〈10.1007/978-3-319-11659-4_1〉
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Contributeur : Clémence Helie <>
Soumis le : mardi 17 mai 2016 - 15:08:45
Dernière modification le : mercredi 18 mai 2016 - 15:11:05

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Carlos Aguilar Melchor, Xavier Boyen, Jean-Christophe Deneuville, Philippe Gaborit. Sealing the Leak on Classical NTRU Signatures. Lecture Notes in Computer Science. 6th International Workshop, PQCrypto 2014, Oct 2014, Waterloo, Canada. springer, 8772, pp.1-21, 2014, Post-Quantum Cryptography. 〈10.1007/978-3-319-11659-4_1〉. 〈hal-01316689〉

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