Pt. 1. Monoalphabetic ciphers using additive alphabets. The Caesar cipher -- Modular arithmetic -- Additive alphabets -- Solution of additive alphabets -- Frequency considerations -- Multiplications -- Solution of multiplicative alphabets -- Affine ciphers -- Pt. 2. General monoalphabetic substitution . Mixed alphabets -- Solution of mixed alphabet ciphers -- Solution of five-letter groupings -- Monoalphabets with symbols -- Pt. 3. Polyalphabetic substitution. Polyalphabetic ciphers -- Recognition of polyalphabetic ciphers -- Determination of number of alphabets -- Solutions of additive subalphabets -- Mixed plain sequences -- Matching alphabets -- Reduction to a monoalphabet -- Mixed cipher sequences -- General comments;Pt. 4. Polygraphic systems. Linear transformations -- Multiplication of matrices -- inverses -- Involutory transformations -- Recognition of digraphic ciphers -- Solution of a linear transformation -- How to make the Hill system more secure -- Pt. 5. Transposition. Columnar transposition -- Completely filled rectangles -- Incompletely filled rectangles -- Probable word method -- General case -- Identical length messages -- Pt. 6. RSA encryption. Public-key encryption -- The RSA method -- Creating the RSA keys -- Why RSA works -- Fermat's Little Theorem -- Computational considerations -- Maple and Mathematica for RSA -- Breaking RSA and signatures -- Pt. 7. Perfect security. One-time pads -- Pseudo-random number generators;In this introduction, Professor Sinkov explains some of the fundamental techniques at the basis of cryptanalytic endeavour from which much more sophisticated techniques have evolved, especially since the advent of computers. Pt. 1. Monoalphabetic ciphers using additive alphabets. The Caesar cipher -- Modular arithmetic -- Additive alphabets -- Solution of additive alphabets -- Frequency considerations -- Multiplications -- Solution of multiplicative alphabets -- Affine ciphers -- Pt. 2. General monoalphabetic substitution . Mixed alphabets -- Solution of mixed alphabet ciphers -- Solution of five-letter groupings -- Monoalphabets with symbols -- Pt. 3. Polyalphabetic substitution. Polyalphabetic ciphers -- Recognition of polyalphabetic ciphers -- Determination of number of alphabets -- Solutions of additive subalphabets -- Mixed plain sequences -- Matching alphabets -- Reduction to a monoalphabet -- Mixed cipher sequences -- General comments Pt. 4. Polygraphic systems. Linear transformations -- Multiplication of matrices -- inverses -- Involutory transformations -- Recognition of digraphic ciphers -- Solution of a linear transformation -- How to make the Hill system more secure -- Pt. 5. Transposition. Columnar transposition -- Completely filled rectangles -- Incompletely filled rectangles -- Probable word method -- General case -- Identical length messages -- Pt. 6. RSA encryption. Public-key encryption -- The RSA method -- Creating the RSA keys -- Why RSA works -- Fermat's Little Theorem -- Computational considerations -- Maple and Mathematica for RSA -- Breaking RSA and signatures -- Pt. 7. Perfect security. One-time pads -- Pseudo-random number generators 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. The book assumes minimal mathematical prerequisites and therefore explains from scratch such concepts as summation notation, matrix multiplication, and modular arithmetic. cryptology cryptography;,cryptanalysis;,cryptology;,number,theory cryptography,cryptanalysis,cryptology,number theory
