## Cryptology ePrint Archive: Report 2011/119

Multiplicative Learning with Errors and Cryptosystems

Gu Chunsheng

Abstract: We introduce a new concept, called multiplicative learning with errors (MLWE), which is a corresponding multiplicative version of the additive learning with errors (LWE), and show the equivalence between the decisional version and the search version for MLWE such that p is a product of sufficiently large smoothing prime factors. Then we construct the MLWE-based private-key and public-key encryption schemes, whose securities are based on the worst-case hardness assumption of the MLWE problem. Finally, we discuss how to extend the LWE on additive group to the LWE on general abelian group.

Category / Keywords: public-key cryptography / Multiplicative Learning with Errors, Private-Key Encryption, Public-key Encryption, LWE on Abelian Group