IACR News item: 25 June 2013
Ciaran Mullan, Boaz Tsaban
ePrint Reportfield 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.
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