Paper 2026/1534 Original: eprint.iacr.org/2026/1534 ↗

Masking, Sequences, and FALCON: A Theoretical Study on Masking Strategies Using Sequences for Non-Linear Operators in the FALCON Post-Quantum Signature

Abstract

Post-Quantum Cryptography is now in its deployment phase. Amongst the threats encountered in real-world applications is Side Channel Analysis, a cryptanalysis branch relying on the study of physical leakages from unsecured implementations. However, the FALCON post-quantum signature includes non-linear functions on real numbers, and applying the generic masking countermeasure to these functions has only been recently studied. In this work, we use convergent sequences to approximate the function and a minimax polynomial to compute the first term of the sequence. The method is applied to the computation of the inverse square root and the square root in FALCON, two operators for which masking has not been investigated before. A theoretical analysis of the security in the t-probing model using the NI criterion and its variants is proposed. Compared to the existing state-of-the-art using the same approach which covers the masked inversion for emulated floating-point implementation, this paper is generic and works with any representation and precision for real numbers.