International Association
for Cryptologic Research

We present a solution to the open problem of designing an efficient, unbiased and timing attack-resistant shuffling algorithm for NTRU fixed-weight sampling. Although it can be implemented without timing leakages of secret data in any architecture, we illustrate with ARMv7-M and ARMv8-A implementations; for the latter, we take advantage of architectural features such as NEON and conditional instructions, which are representative of features available on architectures targeting similar systems, such as Intel. Our proposed algorithm improves asymptotically upon the current approach, which is based on constant-time sorting networks ($O(n)$ versus $O(n \log^2 n)$), and an implementation of the new algorithm is also faster in practice, by a factor of up to $6.91\ (591\%)$ on ARMv8-A cores and $12.58\ (1158\%)$ on the Cortex-M4; it also requires fewer uniform random bits. This translates into performance improvements for NTRU encapsulation, compared to state-of-the-art implementations, of up to 50% on ARMv8-A cores and 71% on the Cortex-M4, and small improvements to key generation (up to 2.7% on ARMv8-A cores and 6.1% on the Cortex-M4), with negligible impact on code size and a slight improvement in RAM usage for the Cortex-M4.