New Techniques for Random Probing Security and Application to Raccoon Signature Scheme

The random probing model formalizes a leakage scenario where each wire in a circuit leaks with probability $p$. This model holds practical relevance due to its reduction to the noisy leakage model, which is widely regarded as the appropriate formalization for power and electromagnetic side-channel attacks.

In this paper, we present new techniques for designing efficient masking schemes that achieve tighter random probing security with lower complexity. First, we introduce the notion of cardinal random probing composability (Cardinal-RPC), offering a new trade-off between complexity and security for composing masking gadgets. Next, we propose a novel refresh technique based on a simple iterative process: randomly selecting and updating two shares with fresh randomness. While not perfectly secure in the standard probing model, this method achieves arbitrary cardinal-RPC security, making it a versatile tool for constructing random-probing secure circuits. Using this refresh, we develop additional basic gadgets (e.g., linear multiplication, addition, and copy) that satisfy the cardinal-RPC notion. Despite the increased complexity, the gains in security significantly outweigh the overhead, with the number of iterations offering useful flexibility.

To showcase our techniques, we apply them to lattice-based signatures. Specifically, we introduce a new random-probing composable gadget for sampling small noise, a key component in various post-quantum algorithms. To assess security in this context, we generalize the random probing security model to address auxiliary inputs and public outputs. We apply our findings to Raccoon, a masking-friendly signature scheme originally designed for standard probing security. We prove the secure composition of our new gadgets for key generation and signature computation, and show that our masking scheme achieves a superior security-performance tradeoff compared to previous approaches based on random probing expansion. To our knowledge, this is the first fully secure instantiation of a post-quantum algorithm in the random probing model.