Fresh re-keying is a recent and promising direction to handle side-channel attacks in cryptographic solutions. It is a simple, plug-in, efficient function that handles the core of side-channel protection directly on the secret key of cryptographic computations. State-of-the-art re-keying schemes can be viewed as a tradeoff between efficient but heuristic solutions based on binary field multiplications, that are only secure if implemented with a sufficient amount of noise, ans formal but more expensive solutions based on weak pseudorandom functions, that remain secure if the adversary accesses their output in full. Recent results on “crypto dark matter” (TCC 2018) suggest that low-complexity pseudorandom functions can be obtained by mixing linear functions over different small moduli. In this paper, we conjecture that by mixing some matrix multiplications in a prime field with a physical mapping similar to the leakage functions exploited in side-channel analysis, we can build efficient re-keying schemes based on “crypto-physical dark matter”, that remain secure against an adversary who can access noise-free measurements. We propose linear re-keying functions which are both more secure and cheaper than previous solutions, and are meant to handle the core part of side-channel resistance in cryptographic functions.
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