Cryptology ePrint Archive: Report 2013/415
Short collision search in arbitrary SL2 homomorphic hash functions
Ciaran Mullan and Boaz Tsaban
Abstract: We study homomorphic hash functions into SL2(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 all concrete
homomorphisms proposed thus far, we prove that
a random homomorphism is at least 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.
For any conceivable practical scenario, our algorithms are substantially faster than all earlier algorithms
and produce much shorter collisions.
Category / Keywords: foundations / SL2 hash, homomorphic hash
Date: received 24 Jun 2013
Contact author: tsaban at math biu ac il
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Version: 20130625:160614 (All versions of this report)
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