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Evaluating NTT/INTT Implementation Styles for Post-Quantum Cryptography

Malik ImranDepartment of Computer Systems, Tallinn University of Technology, Tallinn, EstoniaSafiullah KhanDepartment of Computing and Mathematics, Manchester Metropolitan University, Manchester, U.KAyesha KhalidCentre for Secure Information Technologies, Queen’s University, Belfast, U.KCiara RaffertyCentre for Secure Information Technologies, Queen’s University, Belfast, U.KYasir ShahSchool of Computing, Engineering, and Intelligent Systems at Magee Campus, Ulster University, Londonderry, U.KSamuel PagliariniDepartment of Computer Systems, Tallinn University of Technology, Tallinn, EstoniaMuhammad RashidDepartment of Computer and Network Engineering, College of Computing, Umm Al-Qurrah University, Makkah, Saudi ArabiaMáire O׳NeillCentre for Secure Information Technologies, Queen’s University, Belfast, U.K

2024en

ABI

Annotatsiya

Unifying the forward and inverse operations of the number theoretic transform (NTT) into a single hardware module is a common practice when designing polynomial coefficient multiplier accelerators as used in the post-quantum cryptographic algorithms. This letter experimentally evaluates that this design unification is not always advantageous. In this context, we present three NTT hardware architectures: 1) a forward NTT (FNTT) architecture; 2) an inverse NTT (INTT) architecture; and 3) a unified NTT (UNTT) architecture for computing the FNTT and INTT computations on a single design. We benchmark our throughput/area and energy/area evaluations on Xilinx Virtex-7 field-programmable gate array (FPGA) and 28-nm application-specific integrated circuit (ASIC) platforms. The standalone FNTT and INTT designs, on average on FPGA, exhibit <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.66\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">$3.75\times $ </tex-math></inline-formula> higher throughput/area and energy/area values, respectively, than the UNTT design. Similarly, the individual FNTT and INTT designs, on average on ASIC, achieve <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.25\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">$1.09\times $ </tex-math></inline-formula> higher throughput/area and energy/area values, respectively, compared to the UNTT design.

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DOI: 10.1109/les.2024.3410516

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