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Encryption
An Introduction


Prof. David Bernstein
James Madison University

Computer Science Department
bernstdh@jmu.edu

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Encryption Terminology
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  • Plaintext/Cleartext:
    • Message in its original form
  • Ciphertext:
    • An encrypted message
  • Encryption Algorithm:
    • An algorithm that transforms a message in order to hide its meaning
Symmetric Key Encryption
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images/encryption_symmetric-key.gif
Symmetric Key Encryption (cont.)
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  • Some Classic Algorithms:
    • Caesar Cipher - substitute each letter in the plaintext with the letter shifted a given number of places to the left or right
    • Book Cipher - Replace each letter in the plaintext with three numbers; the page number, line number and character number in a given book
    • Polygraphic Substitution Cipher - divide the plaintext into parts and replace each part with something else (e.g., a word, character, or number)
  • Some Modern (Computer-Based) Algorithms:
    • Data Encryption Standard (DES) - 128, 192, or 256 bit
    • International Data Encryption Algorithm (IDEA)
    • Blowfish
Public Key Encryption
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images/encryption_public-key.gif
Public Key Encryption (cont.)
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Motivating the Rivest-Shamir-Adelman (RSA) Algorithm
  • Encryption/Decryption as a Mapping/Inverse Mapping:
    • If the mapping used for encryption can't be inverted then I can make the mapping public
    • I then need a different mapping for decryption (that I must keep private)
  • Encryption:
    • Convert the plaintext into a number (or numbers) that is less than a predetermined maximum \(n\) (e.g., using the ASCII codes)
    • Multiply the number by itself \(e\) times and use the remainder after dividing by \(n\) as the cyphertext
  • Decryption:
    • Multiply the cyphertext by itself \(d\) times, find the remainder after dividing by \(n\), and convert back to text
Public Key Encryption (cont.)
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Creating Keys with the RSA Algorithm
  1. Select two (large) prime numbers, \(p\) and \(q\)
    • \(p=7\)
    • \(q=17\)
  2. Calculate \(n = p \cdot q \)
    • \(n = 7 \cdot 17 = 119 \)
  3. Find a number, \(e\), that is relatively prime (i.e., has no common divisors with) \((p-1)(q-1)\)
    • \(e = 5\)
  4. Find a number, \(d\), such that \(d \cdot e = 1 \mod (p-1)\cdot(q-1)\) (e.g., using the extended Euclidean algorithm)
    • \(d = 77\)
  5. \(e\) and \(n\) are the public key and \(d\) is the private key
Public Key Encryption (cont.)
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RSA Example
  • Encryption (\(C = P^e \mod n\)):
    • Suppose \(P = 19\)
    • Then \(C = 19^5 \mod 119 = 66\)
  • Decryption (\(P = C^d \mod n\)):
    • Suppose \(C = 66\)
    • Then \(M = 66^{77} \mod 119 = 19\)
There's Always More to Learn
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