Welcome to the resource topic for 2022/1366
Title:
Two remarks on the vectorization problem
Authors: Wouter Castryck, Natan Vander Meeren
Abstract:We share two small but general observations on the vectorization problem for group actions, which appear to have been missed by the existing literature. The first observation is pre-quantum: explicit examples show that, for classical adversaries, the vectorization problem cannot in general be reduced to the parallelization problem. The second observation is post-quantum: by combining a method for solving systems of linear disequations due to Ivanyos with a Kuperberg-style sieve, one can solve the hidden shift problem, and therefore the vectorization problem, for any finite abelian 2^tp^k-torsion group in polynomial time and using mostly classical work; here t, k are any fixed non-negative integers and p is any fixed prime number.
ePrint: https://eprint.iacr.org/2022/1366
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