Verified NTT Multiplications for NISTPQC KEM Lattice Finalists: Kyber, SABER, and NTRU

Abstract

Postquantum cryptography requires a different set of arithmetic routines from traditional public-key cryptography such as elliptic curves. In particular, in each of the lattice-based NISTPQC Key Establishment finalists, every state-ofthe-art optimized implementation for lattice-based schemes still in the NISTPQC round 3 currently uses a different complex multiplication based on the Number Theoretic Transform. We verify the NTT-based multiplications used in NTRU, Kyber, and SABER for both the AVX2 implementation for Intel CPUs and for the pqm4 implementation for the ARM Cortex M4 using the tool CryptoLine. e extended CryptoLine and as a result are able to verify that in six instances multiplications are correct including range properties. We demonstrate the feasibility for a programmer to verify his or her high-speed assembly code for PQC, as well as to verify someone else’s high-speed PQC software in assembly code, with some cooperation from the programmer.

Keywords

• NIST PQC
• NTT
• verification
• NTRU
• Kyber
• Saber