High-Speed Masking for Polynomial Comparison in Lattice-based KEMs

With the NIST post-quantum standardization competition entering the second round, the interest in practical implementation results of the remaining NIST candidates is steadily growing. Especially implementations on embedded devices are often not protected against side-channel attacks, such as differential power analysis. In this regard, the application of countermeasures against side-channel attacks to candidates of the NIST standardization process is still an understudied topic. Our work aims to contribute to the NIST competition by enabling a more realistic judgment of the overhead cost introduced by side-channel countermeasures that are applied to lattice-based KEMs that achieve CCA-security based on the Fujisaki-Okamoto transform. We present a novel higher-order masking scheme that enables an efficient comparison of polynomials as previous techniques based on arithmetic-to-Boolean conversions renders this (generally inexpensive) component extremely expensive in the masked case. Our approach has linear complexity in the number of shares compared to quadratic complexity of previous contributions and it applies to lattice based schemes with prime modulus. It comes with a proof in the probing model and an efficient implementation on an ARM Cortex-M4F microcontroller which was defined as a preferred evaluation platform for embedded implementations by NIST. Our algorithm can be executed in only 1.5-2.2 milliseconds on the target platform (depending on the masking order) and is therefore well suited even for lightweight applications. While in previous work, practical side-channel experiments were conducted using only 5,000 - 100,000 power traces, we confirm the absence of first-order leakage in this work by collecting 1 million power traces and applying the t-test methodology.