Biblio

To protect data in cloud servers, fully homomorphic encryption (FHE) is an effective solution. In addition to encrypting data, FHE allows a third party to evaluate arithmetic circuits (i.e., computations) over encrypted data without decrypting it, guaranteeing protection even during the calculation. However, FHE supports only addition and multiplication. Functions that cannot be directly represented by additions or multiplications cannot be evaluated with FHE. A naïve implementation of such arithmetic operations with FHE is a bit-wise operation that encrypts numerical data as a binary string. This incurs huge computation time and storage costs, however. To overcome this limitation, we propose an efficient protocol to evaluate multi-input functions with FHE using a lookup table. We extend our previous work, which evaluates a single-integer input function, such as f(x). Our extended protocol can handle multi-input functions, such as f(x,y). Thus, we propose a new method of constructing lookup tables that can evaluate multi-input functions to handle general functions. We adopt integer encoding rather than bit-wise encoding to speed up the evaluations. By adopting both permutation operations and a private information retrieval scheme, we guarantee that no information from the underlying plaintext is leaked between two parties: a cloud computation server and a decryptor. Our experimental results show that the runtime of our protocol for a two-input function is approximately 13 minutes, when there are 8,192 input elements in the lookup table. By adopting a multi-threading technique, the runtime can be further reduced to approximately three minutes with eight threads. Our work is more practical than a previously proposed bit-wise implementation, which requires 60 minutes to evaluate a single-input function.

This is a feasibility study on homomorphic encryption using the MK-TFHE library in daily computing using cloud services. Logic gates OR, AND, XOR, XNOR, NOR were created. A basic set of arithmetic operations namely - addition, subtraction, multiplication and division were also created. This research is a continuation of a previous work and this peeks into the newly created logic gates on these arithmetic operations.

The article explores the question of the effective implementation of arithmetic operations with points of an elliptic curve given over a prime field. Given that the basic arithmetic operations with points of an elliptic curve are the operations of adding points and doubling points, we study the question of implementing the arithmetic operations of adding and doubling points in various coordinate systems using the weighted number system and using the Residue Number System (RNS). We have shown that using the fourmodule RNS allows you to get an average gain for the operation of adding points of the elliptic curve of 8.67% and for the operation of doubling the points of the elliptic curve of 8.32% compared to the implementation using the operation of modular multiplication with special moduli from NIST FIPS 186.

Methods for implementing integer arithmetic operations of addition, subtraction, and multiplication in the system of residual classes are considered. It is shown that their practical use in computer systems can significantly improve the performance of the implementation of arithmetic operations. A new method has been developed for raising numbers represented in the system of residual classes to an arbitrary power of a natural number, both in positive and in negative number ranges. An example of the implementation of the proposed method for the construction of numbers represented in the system of residual classes for the value of degree k = 2 is given.

This is a feasibility study on homomorphic encryption using the TFHE library [1] in daily computing using cloud services. A basic set of arithmetic operations namely - addition, subtraction, multiplication and division were created from the logic gates provide. This research peeks into the impact of logic gates on these operations such as latency of the gates and the operation itself. Multiprocessing enhancement were done for multiplication operation using MPI and OpenMP to reduce latency.