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NUMBER THEORY Chapter 5: Cryptology

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Page 1: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

NUMBER THEORY

Chapter 5: Cryptology

Page 2: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

Era of Electronic

• Electronic communication• Electronic Banking

Page 3: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

Terminology

• Cryptology: Discipline • Cryptography: Design & Implementation• Cryptoanalysis: Breaking the system

Page 4: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

Terminology

• Plaintext: secret message • Cipher: method to alter the plaintext• Cybertext: message has been altered

Page 5: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

Terminology

• encryption/enciphering: process• decryption/deciphering: process

Page 6: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

Letter ↔ Integer

Page 7: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

CAESAR CIPHERCharacter Cipher

Page 8: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking
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Exercise

Page 18: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

How to decipher?

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Exercise

Page 25: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

AFFINE TRANSFORMATIONCharacter Cipher

Page 26: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

• Complete system of residue!

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Exercise:

Page 32: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking
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Secure?

• Character cipher is not safe

Page 34: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking
Page 35: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

frequency

Page 36: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking
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VIGENERE CIPHERBlock Cipher

Page 42: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

• Ci=Pi+ki

Page 43: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

Exercise

• Use the key “SECRET”

Page 44: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

DIGRAPHIC CIPHERBlock Cipher

Page 45: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking
Page 46: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

Numerical equivalent

Page 47: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking
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Page 51: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking
Page 52: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

VERNAM CIPHERStream Cipher

Page 53: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking
Page 54: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

AUTOKEY VERNAM CIPHERStream Cipher

Page 55: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking
Page 56: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

Exercise

• Cipher Text

• Seed– F

• Plain Text ?

Page 57: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

EXPONENTIATION CIPHERCryptology

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Page 65: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

Deciphering

Page 66: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

Fermat’s theorem

Page 67: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

• p=2633, e=29

Page 68: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

PUBLIC KEY CRYPTOLOGYCryptology

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RSA Ciphering System

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Page 73: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

Deciphering

• Euclidean Algorithm

Page 74: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking
Page 75: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

Factorizing prime?

• n=pq• What is the factor of following number?•

1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139

Page 76: NUMBER THEORY Chapter 5: Cryptology. Era of Electronic Electronic communication Electronic Banking

• 37975227936943673922808872755445627854565536638199

× 40094690950920881030683735292761468389214899724061


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