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July 17 2018


The two-time pad: midwife of information theory?

The NSA has declassified a fascinating account by John Tiltman, one of Britain’s top cryptanalsysts during world war 2, of the work he did against Russian ciphers in the 1920s and 30s.

In it, he reveals (first para, page 8) that from the the time the Russians first introduced one-time pads in 1928, they actually allowed these pads to be used twice.

This was still a vast improvement on the weak ciphers and code books the Russians had used previously. Tiltman notes ruefully that “We were hardly able to read anything at all except in the case of one or two very stereotyped proforma messages”.

Now after Gilbert Vernam developed encryption using xor with a key tape, Joseph Mauborgne suggested using it one time only for security, and this may have seemed natural in the context of a cable company. When the Russians developed their manual system (which may have been inspired by the U.S. work or a German one-time pad developed earlier in the 1920s) they presumably reckoned that using them twice was safe enough.

They were spectacularly wrong. The USA started Operation Venona in 1943 to decrypt messages where one-time pads had been reused, and this later became one of the first applications of computers to cryptanalysis, leading to the exposure of spies such as Blunt and Cairncross. The late Bob Morris, chief scientist at the NSA, used to warn us enigmatically of “The Two-time pad”. The story up till now was that the Russians must have reused pads under pressure of war, when it became difficult to get couriers through to embassies. Now it seems to have been Russian policy all along.

Many people have wondered what classified war work might have inspired Claude Shannon to write his stunning papers at the end of WW2 in which he established the mathematical basis of cryptography, and of information more generally.

Good research usually comes from real problems. And here was a real problem, which demanded careful clarification of two questions. Exactly why was the one-time pad good and the two-time pad bad? And how can you measure the actual amount of information in an English (or Russian) plaintext telegram: is it more or less than half the amount of information you might squeeze into that many bits? These questions are very much sharper for the two-time pad than for rotor machines or the older field ciphers.

That at least was what suddenly struck me on reading Tiltman. Of course this is supposition; but perhaps there are interesting documents about Shannon’s war work to be flushed out with freedom of information requests. (Hat tip: thanks to Dave Banisar for pointing us at the Tiltman paper.)

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