Lesson 12: Cryptology

1
Lesson 12 Cryptology

• Objectives
• Encode and Decode Using a Caesar cipher
• Encode and Decode Using a Vigenere cipher
• Encode and Decode using the RSA algorithm

• Outline
• Caesar ciphers
• Vigenere ciphers
• RSA algorithm
• Homework Due 3/22
• 2.6 38, 46, 47
• 2.7 4a, 28, 30

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Caesar Cipher

• A Caesar Cipher shifts the alphabet by a distinct
  number of places and encodes all letters with the
  same shift.
• ABCDEFGHIJKLMNOPQRSTUVWXYZ
• DEFGHIJKLMNOPQRSTUVWXYZABC
• VENI
• YHQL

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Caesar Cipher

• The Caesar cipher is a simple shift
• c p s
• to retrieve letter
• p c - s
• Once s is discovered, code is broken
• s can be discovered from frequency analysis

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Caesar Cipher

• Decode the following message
• KDPORDI

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Vigenere Cipher

• Vigenere Ciphers are built on Caesar ciphers, but
  the shift of the Caesar cipher changes with each
  letter.
• This reduces the ability of a code-cracker to
  perform frequency analysis on the ciphertext.
• Need codeword key to know the amount of shifts
  for each letter.

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Vigenere Cipher

• (Vigenere Square)

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Vigenere Cipher

• Decode the following message
• Codeword HAM
• OPEYUXL

8
RSA Encryption

• Based on congruences and factoring of large
  numbers.
• Two keys public and private
• Players
• p,q prime factors of large key
• n product of primes (modulus)
• e exponent which is pairwise prime to (p-1)(q-1)
• M number to be encoded (represents plaintext)
• C encoded number (ciphertext)

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Our public, private key example

• p 43 q 59
• therefore n 43x59 2537
• e found to be 13 (pairwise prime factor for
  exponent)
• gcd(e, (p-1)(q-1)) 1

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Encryption

• Encrypt the word STOP
• S 18, T 19, O14, P15
• STgt 1819, OP gt 1415
• Encrypt each block using the mapping
• C Me mod(n)
• C M13 mod(2537)

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Encryption

• C Me mod(n)
• C1 181913 mod(2537)
• C2 141513 mod(2537)
• Send these encrypted numbers

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RSA Decryption

• find inverse d to e modulo (p-1)(q-1)
• P Cd mod pq

13
Inverse

• Find inverse to 13 modulo 42x58 2436

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Decryption

• We receive 0981 0461. What was the plaintext?
• P Cd mod pq
• P C937 mod (2537)