Evaluating NTT/INTT implementation styles for post-quantum cryptography

Imran, Malik, Khan, Safiullah, Khalid, Ayesha, Rafferty, Ciara, Shah, Yasir Ali, Pagliarini, Samuel, Rashid, Muhammad and O'Neill, Maire (2024) Evaluating NTT/INTT implementation styles for post-quantum cryptography. IEEE Embedded Systems Letters. ISSN 1943-0663

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Abstract

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 work experimentally evaluates that this design unification is not always advantageous. In this context, we present three NTT hardware architectures: (i) A forward NTT (FNTT) architecture, (ii) An inverse NTT (INTT) architecture and (iii) 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 FPGA and 28nm ASIC platforms. The standalone FNTT and INTT designs, on average on FPGA, exhibit 4.66× and 3.75× higher throughput/area and energy/area values respectively than the UNTT design. Similarly, the individual FNTT and INTT designs, on average on ASIC, achieve 1.25× and 1.09× higher throughput/area and energy/area values respectively, compared to the UNTT design.