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Title:
Hardness of Learning Problems over Burnside Groups of Exponent 3
Authors: Nelly Fazio, Kevin Iga, Antonio Nicolosi, Ludovic Perret, William E. Skeith III
Abstract:In this work we investigate the hardness of a computational problem introduced in the recent work of Baumslag et al. In particular, we study the B_n-LHN problem, which is a generalized version of the learning with errors (LWE) problem, instantiated with a particular family of non-abelian groups (free Burnside groups of exponent 3). In our main result, we demonstrate a random self-reducibility property for B_n-LHN. Along the way, we also prove a sequence of lemmas regarding homomorphisms of free Burnside groups of exponent 3 that may be of independent interest.
ePrint: https://eprint.iacr.org/2011/398
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