A bounded-space near-optimal key enumeration algorithm for multi-subkey side-channel attacks

Enumeration of cryptographic keys in order of likelihood based on side-channel leakages has a significant importance in cryptanalysis. The best optimal-order key enumeration algorithms have a huge space complexity of Ω(n^d/2) when there are d subkeys and n candidate values per subkey. In this paper, we present a parallelizable algorithm that enumerates the keys in near-optimal order but enjoys a much better space complexity of O(d²w+dn) for a design parameter w which can be tuned to available RAM. Before presenting our algorithm, we provide lower and upper bounds on the guessing entropy of the full key in terms of the easy-to-compute guessing entropies of the individual subkeys. We use these results to quantify the near-optimality of our algorithm’s ranking, and to bound its guessing entropy. Finally, we evaluate our algorithm through extensive simulations, to show the advantages of our new algorithm in practice, on realistic SCA scenarios. We show that our algorithm continues its nearoptimal- order enumeration far beyond the rank at which the optimal algorithm fails due to insufficient memory.