# Cryptographic History of Work on the German Naval Enigma

the numbers at the head of the columns showing the distance and the entries being the scores, meaning + 4 or 4 in favour of the distance 4 meaning -4 or 4 against the distance.

11. In group (2) there are many possibly relative starting positions, 2 x 675 = 1350 for a pair of messages such as LJR, LXN and 17000 odd for a pair such as LJR, QYN. Individual positions are only therefore worth examining if they are extremely favourable and in practice that means a repeat at least four letters long. The "Tetra Catalogue" prepared by the Hollerith section lists all cases of repeats of four or more letters. A typical series of entries would be

 Trigrams Position Letters AJU 4.8 LK TNSV RAJTLK BYX 6.5 CS TNSV AVYTXK ARX 5.6 AU TNTB LYDRMJ AYR 11.11 XU TNTB LYDACV CRS 6.1 NC TNXJ AVUSYM CQT 8.4 NL TNXJ BRXSTO

The meaning of the entries is fairly clear; in the first example the repeat is TNSV between messages with trigrams AJU, BYZ beginning at the 8th letter in the 4th alphabet of AJU and the 5th letter of the 6th alphabet of BYZ (an alphabet being of course a stretch of 26 letters so that 4.8 indicates the 26 x 3 + 8 = 86th letter of the message). The letters on either side of the repeat show whether or not it extends any further than 4 letters.

12. The first of these three entries is valueless - it is only 4 letters long and the message trigrams having no letters in common has a negligible chance of being right. The second on the other hand is almost certainly right - an 8 letter repeat with the first letter of the trigrams the same is about 1000: 1 on. This is called a "good fit" and is recorded

-98-