Fully Homomorphic Cipher Based on Finite Algebraic Structures

Abstract

A way to increase the robustness of a cryptographic algorithm toward unauthorized inversion can be obtained through application of non-commutative or non-associative algebraic structures. In this regard, data security became a great issue in adaptation of cloud computing over Internet. While in the traditional encryption methods, security to data in storage state and transmission state is provided, in cloud data processing state, decryption of data is assumed, data being available to cloud provider. In this paper, we propose a special homomorphism between self-distributed and non-associative algebraic structures, which can stand as a premise to construct a homomorphic encryption algorithm aimed at the cloud data security in processing state. Homomorphic encryption so developed will allow users to operate encrypted data directly bypassing the decryption.