A permutat ion of the 26-character alphabet is used to encode a sentence with spacing and punctuation intact. Given only the encoded sentence (the "cipher text"), the correct permutat ion is to be found so that the original sentence (the "plain text") can be understood. By framing the problem as a multiple-hypothesis detection problem, applying a maximum-likel ihood criterion, using English language word frequency data, approximat ing liberally, and constructing a well-organized search tree, a ra ther simple algori thm results, which quickly deciphers even difficult cryptograms. Cryptograms of this fo rms imple permutat ion substitutions with word divis ions--have been employed for message concealment, at least, since Roman times. The solution of simple permutat ion ciphers has not been of much practical importance, since their use for military communication was superseded in the nineteenth century, but they remain a formidable puzzle for those who enjoy word games. Experienced solvers can manually solve a typical one-sentence cryptogram in a few minutes, but carefully constructed short puzzles, with unusual letter frequencies or atypical letter combinations, can stymie even expert solvers. Many strategies are published for manual decipherment , e.g., [1-3, 5, 8-10, 12], but these all require human pat tern recognition skills "in the loop," and are not explicit enough to be called algorithms. This author is aware of only one previously published method for automatic so lu t ion-a relaxation method [7], also see [4 ] -bu t it is not suitable for short cryptograms. The solution of a cryptogram can either be given as an explicit sentence of plain text, or it can be characterized by describing the permutat ion that was used to code the plain text. This permutat ion can be inverted then to reconstruct the plain text from the given cipher text. The permutat ion used for this example codes each letter as the letter to its right on the s tandard typewriter keyboard (convenient for touch-typists), with the three letters on the extreme right, (P, L, and M) "wrapping a round" to the left:
[1]
H. Kucera,et al.
Computational analysis of present-day American English
,
1967
.
[2]
Azriel Rosenfeld,et al.
Breaking substitution ciphers using a relaxation algorithm
,
1979,
CACM.
[3]
Harry L. Van Trees,et al.
Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise
,
1992
.
[4]
Alan G. Konheim.
Cryptography, a primer
,
1981
.
[5]
W. W. Ball,et al.
Mathematical Recreations and Essays
,
1905,
Nature.
[6]
Henk C. A. van Tilborg,et al.
An Introduction to Cryptology
,
1988
.
[7]
Claude E. Shannon,et al.
Communication theory of secrecy systems
,
1949,
Bell Syst. Tech. J..
[8]
Abraham Sinkov,et al.
Elementary Cryptanalysis: A Mathematical Approach
,
1970
.
[9]
D. G. N. Hunter,et al.
Experiments with Relaxation Algorithms for Breaking Simple Substitution Ciphers
,
1983,
Comput. J..
[10]
Thomas L. Marzetta,et al.
Detection, Estimation, and Modulation Theory
,
1976
.