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.
Initial attempts to obtain lattice based signatures were closely related to reducing a vector modulo the fundamental parallelepiped of a secret basis (like GGH , or NTRUSign ). This approach leaked some information on the secret, namely the shape of the parallelepiped, which has been exploited on practical attacks . NTRUSign was an extremely efficient scheme, and thus there has been a noticeable interest on developing countermeasures to the attacks, but with little success .
In  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  (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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|Item Type:||Journal Article|
|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|
|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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