Paper 2013/415
SL2 homomorphic hash functions: Worst case to average case reduction and short collision search
Ciaran Mullan and Boaz Tsaban
Abstract
We study homomorphic hash functions into SL(2,q), the 2x2 matrices with determinant 1 over the field with $q$ elements. Modulo a well supported number theoretic hypothesis, which holds in particular for concrete homomorphisms proposed thus far, we provide a worst case to average case reduction for these hash functions: upto a logarithmic factor, a random homomorphism is as secure as _any_ concrete homomorphism. For a family of homomorphisms containing several concrete proposals in the literature, we prove that collisions of length O(log(q)) can be found in running time O(sqrt(q)). For general homomorphisms we offer an algorithm that, heuristically and according to experiments, in running time O(sqrt(q)) finds collisions of length O(log(q)) for q even, and length O(log^2(q)/loglog(q))$ for arbitrary q. While exponetial time, our algorithms are faster in practice than all earlier generic algorithms, and produce much shorter collisions.
Note: To appear in Designs Codes and Cryptography
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Published elsewhere. Unknown status
- Keywords
- SL2 hashhomomorphic hash
- Contact author(s)
- tsaban @ math biu ac il
- History
- 2015-11-02: revised
- 2013-06-25: received
- See all versions
- Short URL
- https://ia.cr/2013/415
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2013/415,
author = {Ciaran Mullan and Boaz Tsaban},
title = {{SL2} homomorphic hash functions: Worst case to average case reduction and short collision search},
howpublished = {Cryptology {ePrint} Archive, Paper 2013/415},
year = {2013},
url = {https://eprint.iacr.org/2013/415}
}