Monoidal Encryption over (𝔽2, ·)

Abstract

In this paper we study monoid homomorphic encryption schemes over (𝔽2, ·). Such encryption schemes occur naturally by forgetting the addition operation in a Ring Homomorphic Encryption scheme over 𝔽2 (if it exists). We study the structure of such schemes and analyze their security against quantum adversaries. We also present the only two monoid homomorphic encryption schemes over (𝔽2, ·) that exist in the literature and we raise the question of the existence of other such schemes. For one of the two schemes we present experimental results that show its performance and efficiency.