Desarrollo de una solución hardware para el esquema de cifrado homomórfico Brakerski-Fan-Vercauteren

Abstract

This work presents the development and implementation of a homomorphic encryption system based on the BFV scheme on a Zynq-7000 FPGA. The system implements the four fundamental operations of the BFV scheme: KeyGen for cryptographic key generation, Encrypt for encrypting messages through modular polynomial operations, Decrypt for recovering the original message through scaling and rounding, and Eval for executing homomorphic operations such as addition and scalar multiplication on encrypted texts. The architecture integrates a true random number generator based on FiGaRO ring oscillators that exploits thermal jitter to generate cryptographic entropy, a pseudorandom generator based on Lorenz and Lü chaotic maps that complements the system's randomness, and a discrete Gaussian noise generator that uses the acceptance-rejection method to produce Gaussian statistical distributions with a standard deviation of 3.2. The system is experimentally validated through the implementation of a homomorphic PID controller for a Buck-Boost converter, where the error signal is processed in the encrypted domain, achieving 99.10% accuracy with a correlation coefficient of 0.9964 between the original and homomorphically processed signals, operating at 100 MHz with encryption times of 41.04 μs and decryption times of 20.56 μs.