Creating a joint secret key in reducing homomorphic encryption for a class of congruent systems

Bezopasnostʹ Informacionnyh Tehnologij

Alla B. Levina¹  Victor Y. Kadykov² 

[1] Saint Petersburg Electrotechnical University "LETI";Saint Petersburg National Research University of Information Technologies, Mechanics and Optics;

关键词: homomorphic encryption, ideal lattices, joint private key, sets theory, information security.;   

DOI  :  10.26583/bit.2021.2.10

来源: DOAJ

【 摘 要 】

Today special attention is paid to homomorphic encryption in the field of information security. Systems of homomorphic encryption represent such systems that allow arbitrary operations over ciphertext that are homomorphic to algebraic operations with plaintext. Some of such systems with ciphertext constructed over ideal lattices are reviewed in the paper. Ideal lattices, in turn, are promising mathematical primitives that allow achieving significant performance as compared to existing encryption systems. In addition, they are resistant to attacks based on quantum computer algorithms. The analysis of sets transforms in the reviewed systems showed that local dependencies and patterns exist between relations of its elements. For congruential encryption class systems, the relation between decryption conditions and noise levels is found. Moreover the private keys of encryption system participants can be hidden in a joint private key which is constructed with the factorial difficulty of recovery. The results can be used for modifying the existing NTRU encryption system and its complementation with homomorphic operations properties discovered recently. The study uses the provisions of set theory, introduces the concept of congruent transition, and deduces the necessary condition for a probabilistic encryption system. The obtained mathematical model is quite simple and allows a generalization of joint private key construction for arbitrary known number operations on a ciphertext. Research is underway to improve the computational efficiency of fully homomorphic encryption systems.

【 授权许可】

Unknown