New records for Playfair solutions

Summary

The Playfair cipher, invented by Charles Wheatstone in 1854 and promoted by Lyon Playfair, encrypts pairs of letters through a 5×5 key square. It was used operationally by British and Commonwealth forces in the Second Boer War and both World Wars. A long-standing cryptanalytic question is: what is the shortest Playfair ciphertext that can be uniquely solved? Before our work the record stood at 26 letters. With Louie Helm, I solved the open 24-letter and 22-letter challenge ciphers — the latter below Deavours’ classic estimate of the Playfair unicity distance, 22.69 letters — and we published the methods at HistoCrypt 2025.

Approach

The attack combines simulated annealing and tabu search over the 25-letter key square with an 8-gram fitness function, then ranks the surviving candidate solutions with a multi-terabyte unpruned n-gram language model. The paper below reports the solved challenges and sets out the parameter choices that made the attack tractable at such short lengths.

Publications and media

Bean, R. and Helm, L. (2025). New records for Playfair solutions. In Proceedings of HistoCrypt 2025.

Conference talk: HistoCrypt 2025, Poznań, 17 June 2025 (L. Helm, presenter).

Related prior work: Bean, R. (2020). The use of Project Gutenberg and hexagram statistics to help solve famous unsolved ciphers. In Proceedings of HistoCrypt 2020.