A Multiplication-Free FPGA Implementation of Multiple RLWE Encryption using Anti-Circulant Matrix

With the expansion of cloud services and privacy security becomes more crucial, fully homomorphic encryption (FHE) scheme which operates data in ciphertext domain has been widely concerned. Lattice-based cryptography ring learning with errors (RLWE), together with its variants RLWE’ and RGSW, form the core component of main-stream homomorphic encryption schemes. This paper presents a universal RLWE encryption module supports ciphertext generation of three cryptographic schemes above. The design uses anti-circulant matrix to convert polynomial multiplication to N-level inner product between vector and anti-circulant matrix to wipe off additional modular reduction. Meanwhile, Montgomery reduction is used to realize multiplicationfree polynomial multiplication. The results show that the utilizations of LUT and FF are reduced by 51% and 30% respectively, as well as completely avoiding DSP usage.