A Tough Nut to Crack :

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• A Tough Nut to Crack
• A look at Cryptography and Codes
• By Joe Mirczuk

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Aims

• Basics
• History
• Methods of cryptography
• Cracking the code?
• Introducing into schools
• Relation to university
• Summary/essay

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Cryptography and Coding Basics

• Cryptography
• Codes
• General Method
• Take message/code word to encrypt plaintext
• Apply encryption/coding technique
• Transmit message
• Decode message/code word using key
• Cryptanalysis

HELLO
001001
Encryption
Encryption
IFMMP
110110
Apply Key
Apply Key
HELLO
001001
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History

• Used throughout history
• Romans
• Second World War
• Computing
• Cryptography all around us
• Keys and locks
• Internet
• CDs/DVDs

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Caesars Cipher
The alphabet is shifted 3 places right in the
cipher

• For example
• Z W
• HELLO EBIIL

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Data Encryption Standard (DES)

• The need for a standard
• DES chosen in 1974 by NIST
• Encryption involving transposition
• - 56-bit key
• - 256 combinations
• 72,057,594,037,927,936 possible keys!
• DES no longer considered secure
• - Testing all keys
• - In 1975 - 100,000 days (300 years)
• - In 2000 - 1 day (100,000 times more powerful)
• Solution?
• - Double DES 2 keys 2112 combinations
• - Triple DES 3 keys 2168 combinations
• - In 2002 - AES

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RSA Encryption

• Method using Public-key cryptography
• - Two keys
• i) Public Key
• ii) Private Key
• - Like a post-box
• Encryption method
• - take two large prime numbers p and q
• - calculate n pq
• - calculate totient F(n) (p-1)(q-1)
• - choose and integer e (encryption exponent)
  such that e and F(n) coprime
• gcd(e, F(n) ) 1
• - calculate d (decryption exponent) such that
• de 1 mod(F(n))
• - public key consists of n and e
• - private key consists of n and d

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RSA (Cont.)
Alice
Bob
Private Key
Public Key
Public Key
Public Key
message
message
Public Key
Private Key
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Cracking the Code

• Spotting the method
• Frequency Analysis
• Brute Force Attack
• - Testing Keys
• Modern Computers

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Schools/University

• In School
• - Writing coded messages
• - Beginners Frequency Analysis
• - Computers

• University
• - RSA a look at modulo arithmetic
• - Frequency analysis
• - 2H Codes

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Summary

• History
• Methods
• Implimentation in schools
• Relevance to university maths
• My essay
• - weaknesses
• - which is most secure?
• - how to increase protection

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Any Questions?