On the Security of the Winternitz One-Time Signature Scheme

Johannes Buchmann; Erik Dahmen; Sarah Ereth; Andreas Hülsing; Markus Rückert

Paper 2011/191

On the Security of the Winternitz One-Time Signature Scheme

Johannes Buchmann, Erik Dahmen, Sarah Ereth, Andreas Hülsing, and Markus Rückert

Abstract

We show that the Winternitz one-time signature scheme is existentially unforgeable under adaptive chosen message attacks when instantiated with a family of pseudo random functions. Compared to previous results, which require a collision resistant hash function, our result provides significantly smaller signatures at the same security level. We also consider security in the strong sense and show that the Winternitz one-time signature scheme is strongly unforgeable assuming additional properties of the pseudo random function. In this context we formally define several key-based security notions for function families and investigate their relation to pseudorandomness. All our reductions are exact and in the standard model and can directly be used to estimate the output length of the hash function required to meet a certain security level.

Note: Eprint report 2017/938 reports a flaw in the security reduction of the proposed construction as well as an issue with the estimation of the exact security which we can confirm. As stated in the report, this flaw does not concern any other variants of WOTS. As we do not see any straight forward way to fix this we suggest to not use the scheme proposed in this work anymore but to use WOTS+.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Full version. An extended abstract of this paper appears in Proceedings of Africacrypt 2011
Keywords: Hash-based signatures post-quantum signatures pseudorandom functions security reductions.
Contact author(s): andreas @ huelsing net
History: 2017-09-28: last of 2 revisions; 2011-04-16: received; See all versions
Short URL: https://ia.cr/2011/191
License: CC BY

BibTeX

@misc{cryptoeprint:2011/191,
      author = {Johannes Buchmann and Erik Dahmen and Sarah Ereth and Andreas Hülsing and Markus Rückert},
      title = {On the Security of the Winternitz One-Time Signature Scheme},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/191},
      year = {2011},
      url = {https://eprint.iacr.org/2011/191}
}