Paper 2023/1373 Original: eprint.iacr.org/2023/1373 ↗

Reframing and Extending the Random Probing Expandibility to Make Probing-Secure Compilers Tolerate a Constant Noise

Abstract

In the context of circuits leaking the internal state due to hardware side-channels, the $p$-random probing model has an adversary who can see the value of each wire with probability $p$. In this model, for a fixed $p$, it is possible to reach an arbitrary security by 'expanding' a stateless circuit via iterated compilation, reaching a security of $2^{-\kappa}$ with a polynomial size in $\kappa$. An artifact of the existing proofs of the expansion is that the worst security is assumed for the input circuit. This means that a pre-compiled input circuit loses all the security guarantees of the first compilation. We reframe the expansion, and we prove it as a security reduction from the compiled circuit to the original one. Additionally, we extend it to support a broader range of encodings, and arbitrary probabilistic gates with an arbitrary number of inputs and outputs. This allows us to prove the following statement: Given a stateless circuit on a field with characteristic $\rho$, and given a $d$-probing secure compiler for some integer $d$, we can produce a circuit with security $2^{-d}$ against any adversary that sees all wires with a constant SD-noise of $2^{-7.41}/\rho$, at the cost of an additional size factor $O(\log(d)^3)$.