On Unpadded NTRU Quantum (In)Security

Théodore Conrad-Frenkiel; Rémi Géraud-Stewart; David Naccache

Paper 2021/1426

On Unpadded NTRU Quantum (In)Security

Théodore Conrad-Frenkiel, Rémi Géraud-Stewart, and David Naccache

Abstract

This paper utilizes the techniques used by Regev \cite{DBLP:journals/jacm/Regev09} and Lyubashevsky, Peikert \& Regev in the security reduction of LWE and its algebraic variants \cite{DBLP:conf/eurocrypt/LyubashevskyPR13} to exhibit a quantum reduction from the decryption of NTRU to leaking information about the secret key. Since this reduction requires decryption with the same key one wishes to attack, it renders NTRU vulnerable to the same type of attacks that affect the Rabin--Williams scheme \cite{DBLP:conf/eurocrypt/Bernstein08} -- albeit requiring a quantum decryption query. A common practice thwarting such attacks consists in applying the Fujisaki-Okamoto (FO, \cite{DBLP:conf/pkc/FujisakiO99}) transformation before encrypting. However, not all NTRU protocols enforce this protection. In particular the DPKE version of NTRU \cite{DBLP:conf/eurocrypt/SaitoXY18} is susceptible to such an attack.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: NTRU cryptanalysis post-quantum cryptography
Contact author(s): david naccache @ ens fr
History: 2021-10-24: received
Short URL: https://ia.cr/2021/1426
License: CC BY

BibTeX

@misc{cryptoeprint:2021/1426,
      author = {Théodore Conrad-Frenkiel and Rémi Géraud-Stewart and David Naccache},
      title = {On Unpadded {NTRU} Quantum (In)Security},
      howpublished = {Cryptology {ePrint} Archive, Paper 2021/1426},
      year = {2021},
      url = {https://eprint.iacr.org/2021/1426}
}