Simpler and More Efficient Rank Estimation for Side-Channel Security Assessment

Rank estimation algorithms allow analyzing the computational security of cryptographic keys for which adversaries have obtained partial information thanks to leakage or cryptanalysis. They are particularly useful in side-channel security evaluations, where the key is known by the evaluator but not reachable with exhaustive search. A first instance of such algorithms has been proposed at Eurocrypt 2013. In this paper, we propose a new tool for rank estimation that is conceptually simpler and much more efficient than this previous proposal. It allows approximating the key rank of (128-bit, 256-bit) symmetric keys with very tight bounds (i.e. with less than one bit of error), almost instantaneously and with limited memory. It also scales nicely to larger (e.g. 1024-bit) key sizes, for which the previous algorithm was hardly applicable.