This note discusses lattice-based cryptography over the field with $p = 2^{64}-2^{32}+1$ elements, with an eye to supporting lattice-based cryptography operations in virtual machines such as Miden VM that operate natively over this field. It discusses how to support Dilithium and Falcon, two lattice-based signature scheme recently selected by the NIST PQC project; and proposes parameters for efficient public key encryption and publicly re-randomizable commitments modulo $p$.

Read the report here or on eprint.