Stopping time signatures for some algorithms in cryptography
This work addresses the problem of algorithm identification in cryptography, but it is incremental as it builds on existing analysis from numerical algorithms.
The paper tackles the problem of characterizing cryptographic algorithms by their running time distributions, extending prior work on numerical algorithms to show that some cryptographic algorithms have indistinguishable time-signatures while others are clearly distinct.
We consider the normalized distribution of the overall running times of some cryptographic algorithms, and what information they reveal about the algorithms. Recent work of Deift, Menon, Olver, Pfrang, and Trogdon has shown that certain numerical algorithms applied to large random matrices exhibit a characteristic distribution of running times, which depends only on the algorithm but are independent of the choice of probability distributions for the matrices. Different algorithms often exhibit different running time distributions, and so the histograms for these running time distributions provide a time-signature for the algorithms, making it possible, in many cases, to distinguish one algorithm from another. In this paper we extend this analysis to cryptographic algorithms, and present examples of such algorithms with time-signatures that are indistinguishable, and others with time-signatures that are clearly distinct.