Cryptology Other Applications of Running-Text Analysis

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Key Re-Use

Consider an (aperiodic or periodic) polyalphabetic cipher that uses the CAESAR operation with help of the TRITHEMIUS table (or addition mod 26), or some other additive encryption such as XOR where Plaintext and key are added letter for letter. (A somewhat more general situation is described in the mathematical version of this section.)

Because the key is not necessarily meaningful text the cryptanalytic methods for running-text ciphers don't apply. But suppose another plaintext is encrypted with the same key. The attacker recognizes this situation by coincidence analysis.

Forming the difference of the two ciphertexts—that the attacker knows—gives the same result as the difference of the two plaintexts—that the attacker wants to know. This difference is a running-text cryptogram (even if it is a difference of two plaintexts instead of a sum—the same methods apply).

Historical Notes

This kind of analysis was a main occupation of the cryptanalysts in World War II and in the following Cold War. In particular teleprinter communication used additive stream ciphers (mostly XOR) with keystreams from key generators and very long periods. In case of heavy message traffic often passages of different messages were encrypted with the key generator in the same state. Searching such passages was called »in-depth-analysis« and relied on coincidence calculations. Then the second step was to subtract the identified passages and to apply running-text analysis.

Some known examples for this are:

• Breaking the Lorenz cipher teleprinter SZ42 (»Schlüsselzusatz«) by the British cryptanalysts at Bletchley Park in World War II (project »Tunny«)[*].
• Breaking Hagelin's B21 in 1931 and the Siemens-Geheimschreiber T52 in 1940 by the Swedish mathematician Arne BEURLING. The T52 was also partially broken at Bletchley Park (project »Sturgeon«).
• The latest politically relevant application of this cryptanalytic technique occurred in the 1950es. US cryptanalysts broke Sovjet ciphertexts and by the way debunked the spy couple Ethel und Julius ROSENBERG (project »Venona«). The Sovjet spys used a one-time pad—in principle. But because key material was rare keys were partly reused.

[*] An illustrative example is in

• Chris Christensen: Review of Lorenz and comments on the work of William Tutte. Cryptologia 42 (2018), 445—466.

Large Periods

Another application is the TRITHEMIUS-BELLASO cipher with a period l large enough that the standard method of arranging the ciphertext in columns and shifting the alphabets fails.

Then the attacker may consider the ciphertext shifted by l positions and subtract it from the original ciphertext. Or, if the key consists of meaningful text, directly treat the cipher as a running-text cipher.

   BOEKV HWXRW VMSIB UXBRK HYQLR OYFWR KODHR JQUMM SJIQA THWSK
   CRUBJ IELLM QSGEQ GSJFT USEWT VTBPI JMPNH IGUSQ HDXBR ANVIS
   VEHJL VJGDS LVFAM YIPJY JM

Hints:

• Find evidence for a period of 38 or 76.
• Try the probable word AMERICA as part of the key.