Originally published in the New Mathematical Library almost half a century ago, this charming book explains how to solve cryptograms based on elementary mathematical principles, starting with the Caesar cipher and building up to progressively more sophisticated substitution methods. Todd Feil has updated the book for the technological age by adding two new chapters covering RSA public-key cryptography, one-time pads, and pseudo-random-number generators.Exercises are given throughout the text that will help the reader understand the concepts and practice the techniques presented. Software to…mehr
Originally published in the New Mathematical Library almost half a century ago, this charming book explains how to solve cryptograms based on elementary mathematical principles, starting with the Caesar cipher and building up to progressively more sophisticated substitution methods. Todd Feil has updated the book for the technological age by adding two new chapters covering RSA public-key cryptography, one-time pads, and pseudo-random-number generators.Exercises are given throughout the text that will help the reader understand the concepts and practice the techniques presented. Software to ease the drudgery of making the necessary calculations is made available. The book assumes minimal mathematical prerequisites and therefore explains from scratch such concepts as summation notation, matrix multiplication, and modular arithmetic. Even the mathematically sophisticated reader, however, will find some of the exercises challenging. (Answers to the exercises appear in an appendix.)
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 Index.
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 Index.
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