“…Based on this state of the art, the main goal of this paper is to provide theoretical explanations for previous empirical observations on prime-field masking, in order to establish foundations on which prime ciphers could be designed. Interestingly, it turns out that the case of bit (e.g., LSB) leakages has been the topic of (for now mostly theoretical) investigations in the context of leakageresilient secret sharing, and extended towards any deterministic leakage model with a bounded range [7,27,31,8,28,30,29]. Among others, these works show that bit leakages are in some sense the most powerful leakage functions with bounded range, which therefore raises the question whether more positive results could be obtained for other, ideally more realistic, leakage functions.…”