As far as I know NTRUSign is considered to be a Post-Quantum scheme but it's vulnerable to the Nguyen-Regev attack that allow to recover private key when there is an access to signature oracle (as it stated in the original paper, 400 message-signature pairs are enough).

After that paper some improvements were proposed and cracked and now NTRUSign seems to be broken.

Do other lattice-based Post-Quantum schemes suffer from the attack by Nguyen-Regev or similar attacks? Signature and key agreement schemes should also be considered.

  • $\begingroup$ If you vote down please describe in comments the reason for that. $\endgroup$
    – CaptainRR
    Commented Jan 17, 2017 at 11:20
  • 1
    $\begingroup$ Just to add: I'm not sure that all NTRU signature proposals are necessarily broken, see for instance eprint.iacr.org/2016/471. Yes, the initial attempts were flawed, but I suppose the standard way to defend against these breaks (rejection sampling) can also be applied to NTRU signatures. Maybe @zhenfei zhang can shed more light on this. $\endgroup$
    – TMM
    Commented Feb 4, 2017 at 14:02

1 Answer 1


NTRUSign does not have a security reduction of the type "if one can break the scheme then one can find short vectors in some lattice." There are several other lattice schemes that do have such a reduction, and are therefore unaffected (as far as we know) by the Nguyen-Regev attack. If they were affected, then we would have a better algorithm fro finding short vectors in lattices.

  • $\begingroup$ Thanks! I'm not familiar with lattice-based crypto and I used to think NTRUSign has reduction to SVP, now it's clear. $\endgroup$
    – CaptainRR
    Commented Jan 18, 2017 at 11:35

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