Non-linear Residue Codes for Robust Public-Key Arithmetic

We present a scheme for robust multi-precision arithmetic over the positive integers, protected by a novel family of non-linear arithmetic residue codes. These codes have a very high probability of detecting arbitrary errors of any weight. Our scheme lends itself well for straightforward implementation of standard modular multiplication techniques, i.e. Montgomery or Barrett Multiplication, secure against active fault injection attacks. Due to the non-linearity of the code the probability of detecting an error does not only depend on the error pattern, but also on the data. Since the latter is not usually known to the adversary a priori, a successful injection of an undetected error is highly unlikely. We give a proof of the robustness of these codes by providing an upper bound on the number of undetectable errors.