Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- 1 Introduction -- Some aspects of secure communication -- Julius Caesar's cipher -- Some basic definitions -- Three stages to decryption: identification, breaking and setting -- Codes and ciphers -- Assessing the strength of a cipher system -- Error detecting and correcting codes -- Other methods of concealing messages -- Modular arithmetic -- Modular addition and subtraction of letters -- Gender -- End matter -- 2 From Julius Caesar to simple substitution -- Julius Caesar ciphers and their solution -- Simple substitution ciphers -- How to solve a simple substitution cipher -- Letter frequencies in languages other than English -- How many letters are needed to solve a simple substitution cipher? -- 3 Polyalphabetic systems -- Strengthening Julius Caesar: Vigenère ciphers -- How to solve a Vigenère cipher -- Indicators -- Depths -- Recognising 'depths' -- How much text do we need to solve a Vigenère cipher? -- Jefferson's cylinder -- 4 Jigsaw ciphers -- Transpositions -- Simple transposition -- Double transposition -- Other forms of transposition -- Regular transposition boxes -- Irregular transposition boxes -- Assessment of the security of transposition ciphers -- Double encipherment in general -- 5 Two-letter ciphers -- Monograph to digraph -- MDTM ciphers -- Digraph to digraph -- Playfair encipherment -- Playfair decipherment -- Cryptanalytic aspects of Playfair -- Double Playfair -- 6 Codes -- Characteristics of codes -- One-part and two-part codes -- Code plus additive -- 7 Ciphers for spies -- Stencil ciphers -- Book ciphers -- Using a book cipher -- Letter frequencies in book ciphers -- Solving a book cipher -- Indicators -- Disastrous errors in using a book cipher -- 'GARBO''S ciphers -- GARBO'S first cipher -- GARBO'S second cipher -- One-time pad.

8 Producing random numbers and letters -- Random sequences -- Producing random sequences -- Coin spinning -- Throwing dice -- Lottery type draws -- Cosmic rays -- Amplifier noise -- Pseudo-random sequences -- Linear recurrences -- Using a binary stream of key for encipherment -- Binary linear sequences as key generators -- Cryptanalysis of a linear recurrence -- Improving the security of binary keys -- Pseudo-random number generators -- The mid-square method -- Linear congruential generators -- 9 The Enigma cipher machine -- Historical background -- The original Enigma -- Encipherment using wired wheels -- Encipherment by the Enigma -- The Enigma plugboard -- The Achilles heel of the Enigma -- The indicator 'chains' in the Enigma -- Aligning the chains -- Identifying R1 and its setting -- Doubly enciphered Enigma messages -- The Abwehr Enigma -- 10 The Hagelin cipher machine -- Historical background -- Structure of the Hagelin machine -- Encipherment on the Hagelin -- Choosing the cage for the Hagelin -- The theoretical 'work factor' for the Hagelin -- Solving the Hagelin from a stretch of key -- Additional features of the Hagelin machine -- The slide -- Identifying the slide in a cipher message -- Overlapping -- Solving the Hagelin from cipher texts only -- 11 Beyond the Enigma -- The SZ42: a pre-electronic machine -- Description of the SZ42 machine -- Encipherment on the SZ42 -- Breaking and setting the SZ42 -- Modifications to the SZ42 -- 12 Public key cryptography -- Historical background -- Security issues -- Protection of programs and data -- Encipherment of programs, data and messages -- The key distribution problem -- The Diffie-Hellman key exchange system -- Strength of the Diffie-Hellman system -- 13 Encipherment and the internet -- Generalisation of simple substitution -- Factorisation of large integers.

The standard method of factorisation -- Fermat's 'Little Theorem' -- The Fermat-Euler Therorem (as needed in the RSA system) -- Encipherment and decipherment keys in the RSA system -- The encipherment and decipherment processes in the RSA system -- How does the key-owner reply to correspondents? -- The Data Encryption Standard (DES) -- Background -- The encipherment procedure -- The decipherment procedure -- Security of the DES -- Chaining -- Implementation of the DES -- Using both RSA and DES -- A salutary note -- Beyond the DES -- Authentication and signature verification -- Elliptic curve cryptography -- Appendix Mathematical aspects -- Chapter 2 -- M1 Identical letters in substitution alphabets -- M2 Reciprocal alphabets weaken security -- M3 The birthdays paradox -- Chapter 3 -- M4 Euclid's proof that there are an infinite number of primes -- Chapter 6 -- M5 The Fibonacci sequence -- Chapter 7 -- M6 Letter frequencies in a book cipher -- M7 One-time pad cipher cannot be solved -- Chapter 8 -- M8 Frequency of occurrence in a page of random numbers -- M9 Combining two biased streams of binary key -- M10 Fibonacci type sequence -- M11 Binary linear recurrences -- M12 Recovery of a binary linear recurrence from a stretch of key -- M13 Generation of pseudo-random numbers -- Chapter 9 -- M14 Wheel wirings in the Enigma -- M15 Number of possible Enigma reflectors -- M16 Probability of a 'depth' in Enigma messages -- M17 Expected number of indicators needed to obtain full chains -- Chapter 10 -- M18 Number of possible Hagelin cages -- M19 Maximum multiple of the kick which can occur when differencing Hagelin key -- M20 Determination of Hagelin slide by correlation coefficient -- Chapter 13 -- M21 (Rate of increase of the number of primes) -- M22 Calculating remainder using modular arithmetic -- M23 Proof of the Fermat-Euler Theorem.

M24 Finding numbers which are 'probably' primes -- M25 The Euclidean Algorithm -- M26 Efficiency of finding powers by repeated squaring -- M27 Expected number of false hits in the 'meet-in-the-middle' attack on the DES -- M28 Elliptic Curve Cryptography -- Solutions to problems -- Chapter 2 -- 2.1 (Simple substitution) -- Chapter 3 -- 3.1 (Three Vigenère messages) -- Chapter 4 -- 4.1 (Simple transposition) -- 4.2 (Number of possible transposition boxes) -- 4.3 (Boustrophedon rows in a transposition box) -- Chapter 5 -- 5.1 (MDTM) -- Chapter 6 -- 6.1 (Fibonacci key) -- Chapter 7 -- 7.1 (Stencil cipher solutions) -- 7.2 (Decrypt of a book cipher) -- 7.3 (Continuation of example solution) -- Chapter 8 -- 8.1 (Recurrences of order 4) -- 8.2 (Cycling in a mid-squares random number generator) -- 8.3 (Cycle lengths in linear congruences) -- Chapter 9 -- 9.1 (Mini-Enigma) -- Chapter 10 -- 10.1 (Hagelin message) -- Chapter 11 -- 11.1 (Pin-setting errors in the Hagelin and SZ42) -- Chapter 13 -- 13.1 (Self-encipherment in the RSA system) -- References -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Chapter 8 -- Chapter 9 -- Chapter 10 -- Chapter 11 -- Chapter 12 -- Chapter 13 -- Name index -- Subject index.