On the Performance and Security of Multiplication in $GF(2^N)$

Multiplications in $GF(2^N)$ can be securely optimized for cryptographic applications when the integer $N$ is small and does not match machine words (i.e., $N < 32$). In this paper, we present a set of optimizations applied to DAGS, a code-based post-quantum cryptographic algorithm and one of the submissions to the National Institute of Standards and Technology’s (NIST) Post-Quantum Cryptography (PQC) standardization call.