Abstract
We introduce a toolkit for transforming lattice-based hash-and-sign signature schemes into masking-friendly signatures secure in the t-probing model. Until now, efficiently masking lattice-based hash-and-sign schemes has been an open problem, with unsuccessful attempts such as Mitaka. A first breakthrough was made in 2023 with the NIST PQC submission Raccoon, although it was not formally proven. Our main conceptual contribution is to realize that the same principles underlying Raccoon are very generic, and to find a systematic way to apply them within the hash-and-sign paradigm. Our main technical contribution is to formalize, prove, instantiate and implement a hash-and-sign scheme based on these techniques. Our toolkit includes noise flooding to mitigate statistical leaks, and an extended Strong Non-Interfering probing security (SNIu) property to handle masked gadgets with unshared inputs. We showcase the efficiency of our techniques in a signature scheme, Plover, based on (hint) Ring-LWE. It is the first lattice-based masked hash-and-sign scheme with quasi-linear complexity O(d log d) in the number of shares d. Our performances are competitive with the state-of-the-art masking-friendly signature, the Fiat-Shamir scheme Raccoon.
