We propose a generalization of the learning parity with noise (LPN) and learning with errors (LWE) problems to an abstract class of group-theoretic learning problems that we term learning homomorphisms with noise (LHN). This class of problems contains LPN and LWE as spe- cial cases, but is much more general. It allows, for example, instantiations based on non-abelian groups, resulting in a new avenue for the applica- tion of combinatorial group theory to the development of cryptographic primitives. We then study a particular instantiation using relatively free groups and construct a symmetric cryptosystem based upon it.
In the 5th International Conference on Provable (ProvSec '11). Xi'an, China, October 16-18, 2011. Springer LNCS 6980, pages 324-339
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