NUMBER THEORY Chapter 5 Cryptology Era of Electronic
NUMBER THEORY Chapter 5: Cryptology
Era of Electronic • Electronic communication • Electronic Banking
Terminology • Cryptology: Discipline • Cryptography: Design & Implementation • Cryptoanalysis: Breaking the system
Terminology • Plaintext: secret message • Cipher: method to alter the plaintext • Cybertext: message has been altered
Terminology • encryption/enciphering: process • decryption/deciphering: process
Letter ↔ Integer
Character Cipher CAESAR CIPHER
Exercise
How to decipher?
Exercise
Character Cipher AFFINE TRANSFORMATION
• Complete system of residue!
Exercise:
Secure? • Character cipher is not safe
frequency
Block Cipher VIGENERE CIPHER
• Ci=Pi+ki
Exercise • Use the key “SECRET”
Block Cipher DIGRAPHIC CIPHER
Numerical equivalent
Stream Cipher VERNAM CIPHER
Stream Cipher AUTOKEY VERNAM CIPHER
Exercise • Cipher Text • Seed –F • Plain Text ?
Cryptology EXPONENTIATION CIPHER
Deciphering
Fermat’s theorem
• p=2633, e=29
Cryptology PUBLIC KEY CRYPTOLOGY
RSA Ciphering System
Deciphering • Euclidean Algorithm
Factorizing prime? • n=pq • What is the factor of following number? • 152260502792253336053561837813263742 9718068114961380688657908494580122963 258952897654000350692006139
• 3797522793694367392280887275544562785 4565536638199 × 4009469095092088103068373529276146838 9214899724061
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