Solution to: Noam Elkies' June 2012 cryptogram for The Enigma 

[*BHBG] *POIRGN, AUIG UGY KYGPOIE BNU, AIUCY *NYISBG SBKLRGY KRTLYI OMRGN MOAPHY MESSYPIE UD RPM KUFRGN IOHY.

Note:  The version actually published included the first word [enclosed in square brackets].  Leaving it out, as was the case for Noam's original version, makes the cryptogram somewhat more difficult to decode.

Solution: Alan Turing, born one century ago, broke German machine cipher using subtle symmetry of its coding rule.

Symmetrical substitution code (in alphabetical order of the earlier letter):  A=B; C=K; D=F; E=Y; G=N; H=L; I=R; M=S; O=U; P=T

Comments from NDE: The version without the first word was the one I submitted—which not only makes it harder but should also draw the solver's attention more emphatically to MESSYPIE as only word with repeated letters (as well as the only "sensible-looking" cipher word).

The choice of letter pairs was more-or-less arbitrary once I chose MESSYPIE as the encryption of "symmetry," and made sure that no letter would code itself. Such pairing is not common either in cryptograms or in actual encrypted communication, but was the "subtle symmetry" that Turing exploited in deciphering the German Enigma. Of course, Enigma was not a simple letter-substitution cipher, but still it had the exact same encryption and decryption algorithms, plus the constraint that, as in a cryptogram, a letter never encoded itself.  Turing was able to take advantage of both of these features/bugs.

Go back to cryptogram (easier version; harder version) or overall "midrash" about A Cryptic Tribute crossword puzzle.