CRYPTOGRPAHY

Explain the following terms clearly with examples.  Each question worth 10 points

For each question, type a minimum one-page double spaced response.

1. Overview of Cryptography and its Application

• Classical Cryptosystems
  • Shift Cipher —Affine Cipher—Substitution Cipher—One-time Pad

• Basic Number Theory
  • Divisibility—-Prime Numbers
  • Greatest Common Divisor
  • Euclidean Algorithm, Extended Euclidean Algorithm
  • Congruence
  • Division
  • Chinese Remainder Theorem
  • Modular Exponential
  • Fermat’s Little Theorem
  • Euler’s Theorem
  • Primitive Roots
  • Finite Fields

• Private-Key (or Secret-Key or Symmetric Key) Cryptography                 
  • A Simplified DES-type Algorithm
  • Differential Cryptanalysis
  • Data Encryption Standards (DES)
  • Breaking DES

• Advanced Encryption Standard (AES)
  • Basic Algorithm
  • Layers
  • ByteSub Transformation
  • ShiftRow Transformation
  • MixColumn Transformation
  • RoundKey Addition
  • Key Schedule
  • Construction of S-Box
  • Decryption

• Public-Key (or Asymmetric Key) Cryptography
  • Public-Key Concept
  • RSA Algorithm
  • Attacks on RSA
    • Low exponent attack
    • Short plaintext
    • Timing attack
  • Primality Testing
  • Factoring
    • Quadratic Sieve
  • Public-Key Infrastructure

• Discrete Logarithm
  • Computing discrete logs
  • Diffie-Hellman key exchange
  • ElGamal Public-Key Cryptosystem

• Hash Functions
  • A simple Hash example
  • Secure Hash Algorithm
  • Birthday Attack

• Digital Signatures
  • RSA Signature
  • ElGamal Signature
  • Hashing & signing
  • DSA
• Applications of Cryptography
  • Digital Cash
  • E-Commerce
• Error Correcting Codes

 Introduction. Error Correcting Codes. Bounds on General Codes. Linear Codes. Hamming Codes. Golay Codes. Cyclic Codes. BCH Codes. Reed-Solomon Codes. The McEliece Cryptosystem

1. Lattice Methods 
   1. Lattices. Lattice Reduction. An Attack on RSA.
2. Investigate Elliptic Curve Cryptosystem
3. Information Theory—Entropy, Huffman Codes, Perfect Secrecy
4. Games—Flipping Coins over the telephone, Poker over the telephone
5. Explore Secret Sharing Schemes
6. Zero-Knowledge Technique—The Feige-Fiat-Shamir Identification Scheme
7. Quantum Techniques in Cryptography
8. Intruders-in-the-Middle and Impostors. Key Distribution. Kerberos 
9. Public Key Infrastructures (PKI). X.509 Certificates. Pretty Good Privacy. SSL and TLS. Secure Electronic Transaction