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Elementary Cryptanalysis

Elementary Cryptanalysis

2nd Edition


Part of Anneli Lax New Mathematical Library

  • Date Published: August 2009
  • availability: Refer to RE Math Assn, Refer to, Mathematical Assn of America, PO BOX 91112, WASHINGTON DC, 20090-112
  • format: Hardback
  • isbn: 9780883856475


Refer to RE Math Assn, Refer to, Mathematical Assn of America, PO BOX 91112, WASHINGTON DC, 20090-112
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About the Authors
  • Most people, acquainted with cryptology either through sensational cloak and dagger stories or through newspaper cryptograms, are not aware that many aspects of this art may be treated systematically, by means of some elementary mathematical concepts and methods. In this introduction, Professor Sinkov explains some of the fundamental techniques at the heart of cryptanalytic endeavor from which much more sophisticated techniques have evolved, especially since the advent of computers. The mathematical topics relevant in these discussions include modular arithmetic, a little number theory, some linear algebra of two dimensions with matrices, some combinatorics, and a little statistics. This second edition has been revised and updated by Todd Fiel, and now includes discussion of the RSA method.

    • Author has professional experience breaking Japanese codes in Second World War
    • Suitable for self-study or course accompaniment
    • Contains exercises and answers
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    Product details

    • Edition: 2nd Edition
    • Date Published: August 2009
    • format: Hardback
    • isbn: 9780883856475
    • length: 224 pages
    • dimensions: 235 x 155 x 16 mm
    • weight: 0.43kg
    • availability: Refer to RE Math Assn, Refer to, Mathematical Assn of America, PO BOX 91112, WASHINGTON DC, 20090-112
  • Table of Contents

    Part I. Monoalphabetic Ciphers:
    1. The Caesar cipher
    2. Modular arithmetic
    3. Additive alphabets
    4. Solution of additive alphabets
    5. Frequency considerations
    6. Multiplications
    7. Solution of multiplicative alphabets
    8. Affine ciphers
    Part II. General Substitution:
    9. Mixed alphabets
    10. Solution of mixed alphabet ciphers
    11. Solution of five-letter groupings
    12. Monoalphabets with symbols
    Part III. Polyalphabetic Substitution:
    13. Polyalphabetic ciphers
    14. Recognition of polyalphabetic ciphers
    15. Determination of number of alphabets
    16. Solutions of additive subalphabets
    17. Mixed plain sequences
    18. Matching alphabets
    19. Reduction to a monoalphabet
    20. Mixed cipher sequences
    21. General comments
    Part IV. Polygraphic Systems:
    22. Linear transformations
    23. Multiplication of matrices - inverses
    24. Involutory transformations
    25. Recognition of digraphic ciphers
    26. Solution of a linear transformation
    27. How to make the Hill system more secure
    Part V. Transposition:
    28. Columnar transposition
    29. Completely filled rectangles
    30. Incompletely filled rectangles
    31. Probable word method
    32. General case
    33. Identical length messages
    Part VI. RSA Encryption:
    34. Public-key encryption
    35. The RSA method
    36. Creating the RSA keys
    37. Why RSA works - Fermat's Little Theorem
    38. Computational considerations
    39. Maple and Mathematica for RSA
    40. Breaking RSA and signatures
    Part VII. Perfect Security - One-Time Pads:
    41. One-time pads
    42. Pseudo-random number generators
    A. Tables
    B. ASCII codes
    C. Binary numbers
    D. Solutions to exercises
    Further readings

  • general resources

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  • Author

    Abraham Sinkov


    Todd Feil

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