Statistical Tests for Randomness on a Typewritten Key Stream Extracted With Computer Vision and Classified With a Convolutional Neural Network

Abstract

For a key stream to be cryptographically secure, it must be sufficiently random (i.e., unpredictable). This study tested the randomness of a set of typewritten, WW2-era German diplomatic key stream tables. Character objects were extracted from images of the tables using computer vision, and a bespoke convolutional neural network (convnet) was trained to classify these objects as digits (from 0–9). The convnet had a mean cross-validated testing balanced accuracy of 93.7% (standard deviation: 0.7%). N = 74,979 digits were extracted and classified from the images. Randomness was tested with the arithmetic mean, chi-squared, runs, and Monte Carlo pi tests; the key stream failed all four tests with 95% confidence. One digit appeared to be over-represented, and two others under-represented in the tables. Analysis suggests that the underrepresented digits may be a simple artefact of computer vision error/bias, but the overrepresented digit did not appear to have resulted from computer vision and/or classification error/bias. Reference streams generated with the Mersenne Twister and Linux OS entropy passed all four tests. WW2-era German diplomatic key stream tables may have lacked randomness. The extent to which this could potentially be exploited by cryptanalysts is unknown.