Proteus: A Pipelined NTT Architecture Generator
Florian Hirner, Ahmet Can Mert, Sujoy Sinha Roy
Abstract
Number theoretic transform (NTT) is a fundamental building block in emerging cryptographic constructions such as fully homomorphic encryption (FHE), post-quantum cryptography (PQC), and zero-knowledge proof (ZKP). In this work, we introduce Proteus, an open-source parametric hardware to generate pipelined architectures for the NTT. For a given parameter set including the polynomial degree and size of the coefficient modulus, Proteus can generate Radix-2 NTT architectures using single-path delay feedback (SDF) and multipath delay commutator (MDC) approaches. We also present a detailed analysis of NTT implementation approaches and use several optimizations to achieve the best NTT configuration. Our evaluations demonstrate performance gain up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.8\times$</tex-math> </inline-formula> compared to SDF and MDC-based NTT implementations in the literature. Our SDF and MDC architectures use <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.75\times$</tex-math> </inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6.5\times$</tex-math> </inline-formula> less DSPs, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times$</tex-math> </inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10.5\times$</tex-math> </inline-formula> less BRAMs, respectively, compared to state-of-the-art SDF and MDC-based NTT implementations.