Statistical cryptanalysis
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Statistical cryptanalysis is not a very common method used by mathematicians but in the modern world it has emerged as a hit-and-try approach. Since the development of cryptology in the industrial and academic worlds in the seventies, public knowledge and expertise have grown in a tremendous way, notably because of the increasing, nowadays almost ubiquitous, presence of electronic communication means in our lives. The methods employed by statistical cryptanalysis are unique to the algorithm or the cipher.
Some well documented statistical cryptanalysis and references:
Block ciphers: Statistical Cryptanalysis of Block Ciphers by P. Junod, PhD thesis number 3179, École Polytechnique Fédérale de Lausanne, Switzerland, 2004.
DES: An experiment on DES statistical cryptanalysis by [Serge Vaudenay]
TEA: A Cryptanalysis of the Tiny Encryption Algorithm by Vikram Reddy Andem, Masters Thesis, Dept of Computer Science, The University of Alabama, Tuscaloosa AL
SEAL: X2 Cryptanalysis of the SEAL Encryption Algorithm Published in E. Biham, Ed., Fast Software Encryption, vol. 1267 of Lecture Notes in Computer Science, pp. 1{12, Springer-Verlag, 1997.