Letter repeats in Enigma ciphertext produced by same-letter keying

Abstract

This paper examines the output ciphertext sequences produced by an Enigma machine that is keyed repeatedly with the same letter. The number of occurrences of runs (subsequences of successive identical characters) of different lengths is counted, and their statistics are compared with what would be expected for an ideal source of independent, equiprobable random letters from a 25-letter alphabet. Unexpectedly high run counts are found for certain rotor configurations; the “extra” runs are shown to arise from particular features of rotor wiring.