International Association
for Cryptologic Research

This paper establishes that the extended Euclidean algorithm (EEA) implemented in a division-free manner is faster than the Lagrange algorithm with a similar level of optimization when it comes to halving the size of scalars found in the equations of elliptic curve signature verification. Our implementation results show that our EEA based method achieves roughly 4x speed-up for generating half- size scalars used in EdDSA. For the first time ever, EEA generated half-size scalars are used for verification of individual Ed25519 signatures yielding timing results that outperform ed25519-donna, a highly optimized open source implementation, by 16.12%. We also propose a new randomization method applied with half-size scalars to batch verification of Ed25519 signatures for which we report speed-ups compared to the well-known Bernstein et al. method for batch sizes larger than six, specifically, our method achieves 11.60% improvement for batch size 64.

This paper proposes various optimizations for lattice-based key encapsulation mechanisms (KEM) using the Number Theoretic Transform (NTT) on the popular ARM Cortex-M4 microcontroller. Improvements come in the form of a faster code using more efficient modular reductions, optimized small-degree polynomial multiplications, and more aggressive layer merging in the NTT, but also in the form of reduced stack usage. We test our optimizations in software implementations of Kyber and NewHope, both round 2 candidates in the NIST post-quantum project, and also NewHope-Compact, a recently proposed variant of NewHope with smaller parameters. Our software is the first implementation of NewHope-Compact on the Cortex-M4 and shows speed improvements over previous high-speed implementations of Kyber and NewHope. Moreover, it gives a common framework to compare those schemes with the same level of optimization. Our results show that NewHope- Compact is the fastest scheme, followed by Kyber, and finally NewHope, which seems to suffer from its large modulus and error distribution for small dimensions.