MODERN CRYPTOGRAPHY: THEORY AND PRACTICE
THE POHLIG-HELLMAN ALGORITHM THE INDEX CALCULUS METHOD LOWER BOUNDS ON THE COMPLEXITY OF GENERIC ALGORITHMS FINITE FIELDS JOUX’S INDEX CALCULUS ELLIPTIC CURVES ELLIPTIC CURVES OVER THE REALS ELLIPTIC CURVES MODULO A PRIME ELLIPTIC CURVES OVER FINITE FIELDS PROPERTIES OF ELLIPTIC CURVES PAIRINGS ON ELLIPTIC CURVES ELGAMAL CRYPTOSYSTEMS ON ELLIPTIC CURVES COMPUTING POINT MULTIPLES ON ELLIPTIC CURVES DISCRETE LOGARITHM ALGORITHMS IN PRACTICE SECURITY OF ELGAMAL SYSTEMS BIT SECURITY OF DISCRETE LOGARITHMS SEMANTIC SECURITY OF ELGAMAL SYSTEMS THE DIF?E-HELLMAN PROBLEMS NOTES AND REFERENCES EXERCISES SIGNATURE SCHEMES INTRODUCTION RSA SIGNATURE SCHEME SECURITY REQUIREMENTS FOR SIGNATURE SCHEMES SIGNATURES AND HASH FUNCTIONS THE ELGAMAL SIGNATURE SCHEME SECURITY OF THE ELGAMAL SIGNATURE SCHEME VARIANTS OF THE ELGAMAL SIGNATURE SCHEME THE SCHNORR SIGNATURE SCHEME THE DIGITAL SIGNATURE ALGORITHM THE ELLIPTIC CURVE DSA FULL DOMAIN HASH CERTI?CATES SIGNING AND ENCRYPTING POST-QUANTUM CRYPTOGRAPHY LATTICE-BASED CRYPTOGRAPHY NTRU LATTICES AND THE SECURITY OF NTRU LEARNING WITH ERRORS CODE-BASED CRYPTOGRAPHY AND THE MCELIECE CRYPTOSYSTEM MULTIVARIATE CRYPTOGRAPHY HIDDEN FIELD EQUATIONS THE OIL AND VINEGAR SIGNATURE SCHEME HASH-BASED SIGNATURE SCHEMES LAMPORT SIGNATURE SCHEME WINTERNITZ SIGNATURE SCHEME MERKLE SIGNATURE SCHEME 10 IDENTI?CATION SCHEMES AND ENTITY AUTHENTICATION 10 1 INTRODUCTION 10 1 1 PASSWORDS 10 1 2 SECURE IDENTI?CATION SCHEMES 10 2 CHALLENGE-AND-RESPONSE IN THE SECRET-KEY SETTING 10 2 1 ATTACK MODEL AND ADVERSARIAL GOALS 10 2 2 MUTUAL AUTHENTICATION 10 3 CHALLENGE-AND-RESPONSE IN THE PUBLIC-KEY SETTING 10 3 1 PUBLIC-KEY IDENTI?CATION SCHEMES 10 4 THE SCHNORR IDENTI?CATION SCHEME 10 4 1 SECURITY OF THE SCHNORR IDENTI?CATION SCHEME 10 5 THE FEIGE-FIAT-SHAMIR IDENTI?CATION SCHEME 10 6 NOTES AND REFERENCES 11 KEY DISTRIBUTION 11 1 INTRODUCTION 11 1 1 ATTACK MODELS AND ADVERSARIAL GOALS 11 2 KEY PREDISTRIBUTION 11 2 1 DIF?E-HELLMAN KEY PREDISTRIBUTION 11 2 2 THE BLOM SCHEME 11 2 3 KEY PREDISTRIBUTION IN SENSOR NETWORKS 11 3 SESSION KEY DISTRIBUTION SCHEMES 11 3 1 THE NEEDHAM-SCHROEDER SCHEME 11 3 2 THE DENNING-SACCO ATTACK ON THE NS SCHEME 11 3 3 KERBEROS 11 3 4 THE BELLARE-ROGAWAY SCHEME 11 4 RE-KEYING AND THE LOGICAL KEY HIERARCHY 11 5 THRESHOLD SCHEMES 11 5 1 THE SHAMIR SCHEME 11 5 2 A SIMPLI?ED (T, T)-THRESHOLD SCHEME 11 5 3 VISUAL THRESHOLD SCHEMES 11 6 NOTES AND REFERENCES 12 KEY AGREEMENT SCHEMES 12 1 INTRODUCTION 12 1 1 TRANSPORT LAYER SECURITY (TLS) 12 2 DIF?E-HELLMAN KEY AGREEMENT 12 2 1 THE STATION-TO-STATION KEY AGREEMENT SCHEME 12 2 2 SECURITY OF STS 12 2 3 KNOWN SESSION KEY ATTACKS 12 3 KEY DERIVATION FUNCTIONS 12 4 MTI KEY AGREEMENT SCHEMES 12 5 DENIABLE KEY AGREEMENT SCHEMES 12 6 KEY UPDATING 12 7 CONFERENCE KEY AGREEMENT SCHEMES 12 8 NOTES AND REFERENCES 13 MISCELLANEOUS TOPICS 13 1 IDENTITY-BASED CRYPTOGRAPHY 13 1 1 THE COCKS IDENTITY-BASED CRYPTOSYSTEM 13 1 2 BONEH-FRANKLIN IDENTITY-BASED CRYPTOSYSTEM 13 2 THE PAILLIER CRYPTOSYSTEM 13 3 COPYRIGHT PROTECTION 13 3 1 FINGERPRINTING 13 3 2 IDENTI?ABLE PARENT PROPERTY 13 3 3 2-IPP CODES 13 3 4 TRACING ILLEGALLY REDISTRIBUTED KEYS 13 4 BITCOIN AND BLOCKCHAIN TECHNOLOGY 13 5 NOTES AND REFERENCES CHAPTER SECRET-KEY CRYPTOSYSTEMS CRYPTOGRAPHY HAS BEEN USED FOR THOUSANDS OF YEARS TO HELP TO PROVIDE CON?- DENTIAL COMMUNICATIONS BETWEEN MUTUALLY TRUSTED PARTIES IN ITS MOST BASIC FORM, TWO PEOPLE, OFTEN DENOTED AS ALICE AND BOB, HAVE AGREED ON A PARTICULAR SECRET KEY AT SOME LATER TIME, ALICE MAY WISH TO SEND A SECRET MESSAGE TO BOB (OR BOB MIGHT WANT TO SEND A MESSAGE TO ALICE) THE KEY IS USED TO TRANSFORM THE ORIGINAL MESSAGE (WHICH IS USUALLY TERMED THE PLAINTEXT) INTO A SCRAMBLED FORM THAT IS UNINTELLIGIBLE TO ANYONE WHO DOES NOT POSSESS THE KEY THIS PROCESS IS CALLED ENCRYPTION AND THE SCRAMBLED MESSAGE IS CALLED THE CIPHERTEXT WHEN BOB RECEIVES THE CIPHERTEXT, HE CAN USE THE KEY TO TRANSFORM THE CIPHERTEXT BACK INTO THE ORIGINAL PLAINTEXT; THIS IS THE DECRYPTION PROCESS A CRYPTOSYSTEM CONSTITUTES A COMPLETE SPECI?CATION OF THE KEYS AND HOW THEY ARE USED TO ENCRYPT AND DECRYPT INFORMATION VARIOUS TYPES OF CRYPTOSYSTEMS OF INCREASING SOPHISTICATION HAVE BEEN USED FOR MANY PURPOSES THROUGHOUT HISTORY IMPORTANT APPLICATIONS HAVE INCLUDED SENSI- TIVE COMMUNICATIONS BETWEEN POLITICAL LEADERS AND/OR ROYALTY, MILITARY MANEU- VERS, ETC HOWEVER, WITH THE DEVELOPMENT OF THE INTERNET AND APPLICATIONS SUCH AS ELECTRONIC COMMERCE, MANY NEW DIVERSE APPLICATIONS HAVE EMERGED THESE IN- CLUDE SCENARIOS SUCH AS ENCRYPTION OF PASSWORDS, CREDIT CARD NUMBERS, EMAIL, DOC- UMENTS, ?LES, AND DIGITAL MEDIA