Encryption

Encryption
An Introduction

Computer Science Department

bernstdh@jmu.edu

Encryption Terminology

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

Symmetric Key Encryption (cont.)

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

Public Key Encryption (cont.)

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.)

Creating Keys with the RSA Algorithm

Select two (large) prime numbers, p and q
- $p=7$
- $q=17$
Calculate n = p \cdot q
- $n = 7 \cdot 17 = 119$
Find a number, e, that is relatively prime (i.e., has no common divisors with) (p-1)(q-1)
- $e = 5$
Find a number, d, such that d \cdot e = 1 \mod (p-1)\cdot(q-1) (e.g., using the extended Euclidean algorithm)
- $d = 77$
$e$ and $n$ are the public key and $d$ is the private key

Public Key Encryption (cont.)

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 $M = 66^{77} \mod 119 = 19$

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