American Scientist

To the Editors:

In his article “A Cipher to Thomas Jefferson” (March–April) Lawren M. Smithline states that solving substitution ciphers is possible by frequency analysis or counting the number of occurrences of each letter of the alphabet in a message. This may often be true, but Smithline or I would be able to decipher the tongue twister “Peter Piper picked a peck of pickled peppers” if it were encoded by a substitution cipher, despite the wildly skewed frequency distribution of letters. The single-letter word “a” would be immediately identified as very probably being either “a” or “I”, and the message would be deciphered by sequentially replacing instances of whatever letter replaces “p” in the cipher with various letters and considering if the resulting partially-solved cipher could readily be fully deciphered, despite that the second-most common letter “t” occurs only once, and “a” occurs with a lower frequency than “i.”

Marshall E. Deutsch
Sudbury, MA

Dr. Smithline responds:

I know of a book, A Void, a translation of La Disparition. Both omit that fifth in our list of writing symbols. A paragraph probably would show unusual counts. Drafting such a composition, a lipogram, is difficult.

Letter counts from long samples of unaffected English tend to conform to a standard frequency table. Short or contrived messages may show letter counts not conforming to the standard table. Solvers of newspaper cryptograms know that if spaces are left between words, then it is possible to make inferences from one-letter words, two-letter words, the first letters of words, and so on.