Sealing the leak on classical NTRU signatures

Aguilar Melchor, Carlos, Boyen, Xavier, Deneuville, Jean-Christophe, & Gaborit, Philippe (2014) Sealing the leak on classical NTRU signatures. Lecture Notes in Computer Science, 8772, pp. 1-21.

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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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ID Code: 82284
Item Type: Journal Article
Refereed: Yes
Additional Information: Post-Quantum Cryptography : 6th International Workshop, PQCrypto 2014, Waterloo, ON, Canada, October 1-3, 2014. Proceedings, Print ISBN 978-3-319-11658-7
Keywords: Lattice-based cryptography, Digital signatures, NTRUSign, Provable security, SIS
DOI: 10.1007/978-3-319-11659-4_1
ISSN: 0302-9743
Divisions: Current > Schools > School of Electrical Engineering & Computer Science
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 Springer International Publishing Switzerland
Deposited On: 06 Mar 2015 01:30
Last Modified: 08 Mar 2015 22:11

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