Elementary Cryptanalysis

by Sinkov, Abraham; Feil, Todd

• ISBN13: 9780883856475
• ISBN10: 0883856476
• Edition: 2nd
• Format: Hardcover
• Copyright: 2009-07-16
• Publisher: Mathematical Assn of Amer

Summary

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.

Table of Contents

Monoalphabetic Ciphers

The Caesar cipher

Modular arithmetic

Additive alphabets

Solution of additive alphabets

Frequency considerations

Multiplications

Solution of multiplicative alphabets

Affine ciphers

General Substitution

Mixed alphabets

Solution of mixed alphabet ciphers

Solution of five-letter groupings

Monoalphabets with symbols

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

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

Transposition

Columnar transposition

Completely filled rectangles

Incompletely filled rectangles

Probable word method

General case

Identical length messages

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

Perfect Security - One-Time Pads

One-time pads

Pseudo-random number generators

Tables

ASCII codes

Binary numbers

Solutions to exercises

Further readings

Index

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