CODES AND CIPHERS

By X. LUURR

CONTENTS 1 INTRODUCTION SOME ASPECTS OF SECURE COMMUNICATION JULIUS CAESAR’S CIPHER SOME BASIC DE?NITIONS THREE STAGES TO DECRYPTION: IDENTI?CATION, 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 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 LETTER FREQUENCIES IN BOOK CIPHERS SOLVING A BOOK CIPHER DISASTROUS ERRORS IN USING A BOOK CIPHER ‘GARBO’’S CIPHERS ONE-TIME PAD 8 PRODUCING RANDOM NUMBERS AND LETTERS RANDOM SEQUENCES PRODUCING RANDOM SEQUENCES COIN SPINNING THROWING DICE LOTTERY TYPE DRAWS COSMIC RAYS AMPLI?ER NOISE PSEUDO-RANDOM SEQUENCES LINEAR RECURRENCES USING A BINARY STREAM OF KEY FOR ENCIPHERMENT BINARY LINEAR SEQUENCES AS KEY GENERATORS CONTENTS 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 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 MODI?CATIONS TO THE SZ42 12 PUBLIC KEY CRYPTOGRAPHY SECURITY ISSUES PROTECTION OF PROGRAMS AND DATA ENCIPHERMENT OF PROGRAMS, DATA AND MESSAGES CONTENTS THE KEY DISTRIBUTION PROBLEM THE DIF?E–HELLMAN KEY EXCHANGE SYSTEM STRENGTH OF THE DIF?E–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 THEOREM (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) SECURITY OF THE DES CHAINING IMPLEMENTATION OF THE DES USING BOTH RSA AND DES A SALUTARY NOTE BEYOND THE DES AUTHENTICATION AND SIGNATURE VERI?CATION ELLIPTIC CURVE CRYPTOGRAPHY