Cryptology ePrint Archive: Report 2011/398

Hardness of Learning Problems over Burnside Groups of Exponent 3

Nelly Fazio and Kevin Iga and Antonio Nicolosi and Ludovic Perret and 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.

Category / Keywords: foundations / Random self-reducibility. Learning with errors. Post-quantum cryptography. Non-commutative cryptography. Burnside groups.

Date: received 25 Jul 2011, last revised 19 May 2012

Contact author: wes at cs ccny cuny edu

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Version: 20120519:195915 (All versions of this report)

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