difficult to cryptanalyse; each variant required different cryptanalytic treatment. The commercial versions were not as secure and Dilly Knox of GC&CS is said to have broken one before the war. German military Enigma was first broken in December 1932 by the Polish Cipher Bureau, using a combination of brilliant mathematics, the services of a spy in the German office responsible for administering encrypted communications, and good luck. The Poles read Enigma to the outbreak of World War II and beyond, in France. At the turn of 1939, the Germans made the systems ten times more complex, which required a tenfold increase in Polish decryption equipment, which they could not meet. On 25 July 1939, the Polish Cipher Bureau handed reconstructed Enigma machines and their techniques for decrypting ciphers to the French and British. Gordon Welchman wrote, At Bletchley Park, some of the key people responsible for success against Enigma included mathematicians Alan Turing and Hugh Alexander and, at the British Tabulating Machine Company, chief engineer Harold Keen. After the war, interrogation of German cryptographic personnel led to the conclusion that German cryptanalysts understood that cryptanalytic attacks against Enigma were possible but were thought to require impracticable amounts of effort and investment. The Poles' early start at breaking Enigma and the continuity of their success gave the Allies an advantage when World War II began. Lorenz cipher In June 1941, the Germans started to introduce on-line stream cipher teleprinter systems for strategic point-to-point radio links, to which the British gave the code-name Fish. Several systems were used, principally the Lorenz SZ 40/42 (Tunny) and Geheimfernschreiber (Sturgeon). These cipher systems were cryptanalysed, particularly Tunny, which the British thoroughly penetrated. It was eventually attacked using Colossus machines, which were the first digital programme-controlled electronic computers. In many respects the Tunny work was more difficult than for the Enigma, since the British codebreakers had no knowledge of the machine producing it and no head-start such as that the Poles had given them against Enigma. Although the volume of intelligence derived from this system was much smaller than that from Enigma, its importance was often far higher because it produced primarily high-level, strategic intelligence that was sent between Wehrmacht High Command (OKW). The eventual bulk decryption of Lorenz-enciphered messages contributed significantly, and perhaps decisively, to the defeat of Nazi Germany. Nevertheless, the Tunny story has become much less well known among the public than the