International Association
for Cryptologic Research

The topic of verifying postquantum cryptographic software has never been more pressing than today between the new NIST postquantum cryptosystem standards being finalized and various countries issuing directives to switch to postquantum or at least hybrid cryptography in a decade. One critical issue in verifying lattice-based cryptographic software is range-checking in the finite-field arithmetic assembly code which occurs frequently in highly optimized cryptographic software. For the most part these have been handled by Satisfiability Modulo Theory (SMT) but so far they mostly are restricted to Montgomery arithmetic and 16-bit precision. We add semi-automatic range-check reasoning capability to the CryptoLine toolkit via the Integer Set Library (wrapped via the python package islpy) which makes it easier and faster to verify more arithmetic crypto code, including Barrett and Plantard finite-field arithmetic, and show experimentally that this is viable on production code.

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.