TY - UNPB
T1 - Short collision search in arbitrary SL2 homomorphic hash functions.
AU - Mullan, Ciaran
AU - Tsaban, Boaz
N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2013
Y1 - 2013
N2 - 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.Related DOI:https://doi.org/10.1007/s10623-015-0129-8
AB - 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.Related DOI:https://doi.org/10.1007/s10623-015-0129-8
U2 - https://doi.org/10.48550/arXiv.1306.5646
DO - https://doi.org/10.48550/arXiv.1306.5646
M3 - نسخة اولية
VL - abs/1306.5646
BT - Short collision search in arbitrary SL2 homomorphic hash functions.
ER -