Paper 2024/1163
On the Number of Restricted Solutions to Constrained Systems and their Applications
Abstract
In this paper, we formulate a special class of systems of linear equations over finite fields and derive lower bounds on the number of solutions adhering to some predefined restrictions. We then demonstrate the applications of these lower bounds to derive tight PRF security (up to $2^{3n/4}$ queries) for single-keyed variants of the Double-block Hash-then-Sum (DBHtS) paradigm, specifically PMAC+ and LightMAC+. Additionally, we show that the sum of $r$ independent copies of the Even-Mansour cipher is a secure PRF up to $2^{\frac{r}{r+1}n}$ queries.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Preprint.
- Keywords
- PMAC+LightMAC+Sum of Even-Mansourtight security
- Contact author(s)
-
benoit cogliati @ gmail com
jordan ethan @ cispa de
letterstoashwin @ gmail com
mridul nandi @ gmail com
sahaa 1993 @ gmail com - History
- 2024-07-19: approved
- 2024-07-18: received
- See all versions
- Short URL
- https://ia.cr/2024/1163
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/1163, author = {Benoît Cogliati and Jordan Ethan and Ashwin Jha and Mridul Nandi and Abishanka Saha}, title = {On the Number of Restricted Solutions to Constrained Systems and their Applications}, howpublished = {Cryptology ePrint Archive, Paper 2024/1163}, year = {2024}, note = {\url{https://eprint.iacr.org/2024/1163}}, url = {https://eprint.iacr.org/2024/1163} }