Basic Cryptography

Basic Cryptography Notes

Introduction to Cryptography

• Cryptography: The study of secure communications, encompassing both cryptography and cryptanalysis.
  • Cryptology: Study of secure communications.
  • Cipher: An algorithm for encryption/decryption.
  • Plain Text: Original form of a message.
  • Cipher Text: Encrypted form of a message.

Importance of Encryption

• Secrecy or Confidentiality: Keeps information secret.
• Accuracy or Integrity: Encryption can protect against forgery or tampering.
• Authenticity: Digital signatures ensure authenticity in transactions.

Methods of Defense

• Software Controls:
  • Internal program controls
  • Operating system controls
  • Development controls
• Hardware Controls:
  • Firewalls
  • Intrusion Detection Systems
• Effectiveness of Controls:
  • Awareness of Problem
  • Likelihood of Use
  • Overlapping Controls
  • Periodic Review

Types of Encryption

• Symmetric Encryption:
  • Same key for encryption and decryption.
  • Example: C = E(K, P)
• Asymmetric Encryption:
  • Different keys for encryption and decryption (public/private key pair).
  • Example: P = D(KD, E(KE, P))

Encryption Algorithms

• Secret Key (Symmetric System): Shared key for two users.
  • Key distribution is a challenge.
• Public Key (Asymmetric System):
  • Public key for encryption; private key for decryption.
  • n(n-1)/2 keys needed for n users.

Cryptanalysis

• Techniques to break encryption:
  • Breaking a single message.
  • Recognizing patterns.
  • Finding algorithm weaknesses.

Modular Arithmetic in Cryptography

• Represents letters as numbers (A=0, B=1, C=2…).
• Allows calculations with letters (e.g., A + 3 = D).

Monoalphabetic Ciphers

• Caesar Cipher:
  • Each letter shifts a fixed number (e.g., +3).
  • Example: TREATY -> WUHDWB.
  • Advantages: Easy to perform; disadvantages: pattern is predictable.
• Substitutions:
  • Each character corresponds to another character.

Permutations in Cryptography

• Scrambled alphabet for encryption.
• Provides a unique ciphertext letter for each plaintext letter.
  • Example Permutation: ABCDEFGHIJKLMNOPQRSTUVWXYZ -> CBADEFGHIJKLMNOPQRSTUVWXYZ.

Polyalphabetic Ciphers

• Combines multiple monoalphabetic ciphers to improve security.
• Vigenère Cipher:
  • Uses a table for encryption based on keys.
  • Aims to flatten frequency distribution of letters.

Kasiski Method for Cryptanalysis

• Identifies repeated patterns in ciphertext to determine key length.
• Involves computing distances between these patterns.

Index of Coincidence

• Measures variation between letter frequencies in a ciphertext.
• Helps predict the number of substitutions used.

Perfect Substitution Cipher

• Requires non-repeating and infinite sequence for better security.
• One-Time Pads: Uses a unique key for only one use; provides ultimate secrecy but requires synchronization.

Summary of Key Concepts

• Substitutions: Monoalphabetic and Polyalphabetic Ciphers
• Transpositions: Permutations used for block ciphers.
• Vigenère Tableaux: Extends permutations to improve frequency distribution.
• One-Time Pads: Considered the most secure, but challenging to implement effectively.