Kyber terminates

Manuel Barbosa; Peter Schwabe

Paper 2023/708

Kyber terminates

Manuel Barbosa

, University of Porto, INESC TEC

Peter Schwabe

, Max Planck Institute for Security and Privacy, Radboud University

Abstract

The key generation of the lattice-based key-encapsulation mechanism CRYSTALS-Kyber (or short, just Kyber) involves a rejection-sampling routine to produce coefficients modulo $q=3329$ that look uniformly random. The input to this rejection sampling is output of the SHAKE-128 extendable output function (XOF). If this XOF is modelled as a random oracle with infinite output length, it is easy to see that Kyber terminates with probability 1; also, in this model, for any upper bound on the running time, the probability of termination is strictly smaller than 1. In this short note we show that an (unconditional) upper bound for the running time for Kyber exists. Computing a tight upper bound, however, is (likely to be) infeasible. We remark that the result has no real practical value, except that it may be useful for computer-assisted reasoning about Kyber using tools that require a simple proof of termination.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Contact author(s): mbb @ fc up pt
peter @ cryptojedi org
History: 2023-05-22: approved; 2023-05-17: received; See all versions
Short URL: https://ia.cr/2023/708
License: CC0

BibTeX

@misc{cryptoeprint:2023/708,
      author = {Manuel Barbosa and Peter Schwabe},
      title = {Kyber terminates},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/708},
      year = {2023},
      url = {https://eprint.iacr.org/2023/708}
}