A million-bit multiplier architecture for fully homomorphic encryption

In this work we present a full and complete evaluation of a very large multiplication scheme in custom hardware. We designed a novel architecture to realize a million-bit multiplication scheme based on the Schönhage-Strassen Algorithm. We constructed our scheme using Number Theoretical Transform (NTT). The construction makes use of an innovative cache architecture along with processing elements customized to match the computation and access patterns of the NTT-based recursive multiplication algorithm. We realized our architecture with Verilog and using a 90 nm TSMC library, we could get a maximum clock frequency of 666 MHz. With this frequency, our architecture is able to compute the product of two million-bit integers in 7.74 ms. Our data shows that the performance of our design matches that of previously reported software implementations on a high-end 3 GHz Intel Xeon processor, while requiring only a tiny fraction of the area.