Cryptanalysis of Hagelin machine pin wheels

Cryptologia, Oct 2002 by Sullivan, Geoff

The use of the letter Z as a word spartor was found to have no influence on results.

Some previous accounts of ciphertext-only statistical cryptanaylsis of the M209 have also indicated that about 2000 characters are required to achieve success [1, p. 1221, [4, p. 31]. The CD-57 with its greater wheel length would require a longer message, possibly above 4000 characters. The simpler lug settings of this machine, which involve no sharing between wheels, would be expected to give better results for the lug numbers. It is unlikely that messages of this length would be enciphered on such a machine, which has no printing facility.

The alphabet ring of the CD-57 is normally a reversed alphabet, so either ring can be used for encryption or decryption. However it is possible to arrange a random alphabet on the outer stationary ring and also to offset this ring to 26 different positions. The Author has not attempted to attack these configurations. Some later models of Hagelin pin and lug machine incorporated additional lug bars to control the stepping of some of the wheels. Hillclimbing would not work for these machines since pin errors would throw the machine out of step.

ACKNOWLEDGEMENTS

I thank Jim Gillogly for introducing me to the application of hillclimbing to classical ciphers, Frode Weierud for a review of this paper and help with documents. Without his initial encouragement I may never have started on this project.

1A discussion group, with public archive, for the Cipher Challenge can be found at http://groups.yahoo. com/group/CipherChallenge. Gillogly's method was discussed at length in this group.

2For a review of this book (5] see Notices of the AMS March 2000: 329-371 or www. ams.org/notices search.

3In the 1977 Cryptologia article [3], wheel 38 is omitted from the CD -57 wheel list due to a transcription error.

4 Jane Eyre by Charlotte Bronte (1816-1855) can be found in electronic form at the 'gutenberg Project: http://promo.net/pg

44

7See Appendix A.

8Not all arrangements are practical, nevertheless the actual number is very large.

REFERENCES

1. Beker, H. and F. Piper. 1982. Cipher Systems: The Protection of Communications. London. Northwood Books.

2. Crypto AG. Undated. Pocket Cryptographer Type CD-57 Operation Instructions. Zug SWITZERLAND: Crypto AG.

3. Kruh, L. 1977. Cipher Equipment: Hagelin Pocket Cryptographer, Type CD-57. Cryptologia. 1(3): 255-260.

4. Rivest, R. 1981. Statistical Analysis of the Hagelin Cryptograph. Cryptologia. 5(1): 27-30.

5. Singh, S. 1999. The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography. London: Fourth Estate.

6. Sinkov, A. 1966. Elementary Cryptanalysis. Washington DC: The Mathematical Association of America.

7. Spillman, R., M. Janssen, B. Nelson, and M. Kepner. 1993. Use of a Genetic Algorithm in the Cryptanalysis of Simple Substitution Ciphers. Cryptologia. 17(1): 31-44.

8. War Department. 1942. TM-11-380 Technical Manual. Washington: War Department. A copy of this manual in HTML format can be found at http://www.maritime.org/cspl500inst.htm.