MCS 425 Course Information
Spring Semester, 2008

MCS 425  Syllabus
Fall Semester, 2006

• Introduction to encoding / decoding of information
  • Reasons for encoding / decoding
    • Efficiency (data compression)
    • Reliability (error detection and correction)
    • Security (encryption and digital signatures

• Chap 1:  Overview of cryptography and its applications

  • Sec 1.1    Secure communications, attacks on encryption algorithms, Kerckhoffs's principle, symmetric-key (private-key) vs public key algorithms.

  • Sec 1.2    Cryptographic applications

  Chap 2:  Classical cryptosystems

  • Sec 2.1    Shift ciphers.
  • Sec 2.2    Affine ciphers.
  • Sec 2.4    Substitution ciphers.
  • --------    Transposition ciphers (brief discussion).
  • Sec 2.8    Binary numbers and ASCII; and, or, and xor operations; properties of xor.
  • Sec 2.9    One-time pads.
  • Sec 2.10  Pseudo-random bit generation.

• Chap 3:  Basic number theory for cryptography and coding theory

  • Sec 3.1    Basic notions:  Divisibility, primes, density of primes, unique factorization, gcd, Euclid's algorithm, inverses mod m.
  • Sec 3.2    Solving ax + by = d (a, b, c, d
  • Sec 3.3    Congruences, the integers modulo m, multiplicative inverses modulo m.
  • Sec 3.4    The Chinese Remainder Theorem.  Applications to finding square roots mod m.
  • Sec 3.5    Fast modular exponentiation.
  • Sec 3.6    Fermat's Little Theorem, Euler's phi-function and Euler's Theorem; the 3-pass protocol.
  • Sec 3.7    Primitive roots.
  • Sec 3.9    Square roots mod n.
  • Sec 3.11  Finite fields.

• Chap 4:  Feistel ciphers and the The Data Encryption Standard (DES)

  • Sec 4.1    Introduction.  Private-key cryptography.  Block vs stream ciphers.
  • Sec 4.2    Feistel ciphers.  P-boxes and S-boxes.  A simplified DES-type algorithm.
  • Sec 4.4    The DES algorithm.
  • Sec 4.5    Modes of operation (ECB, CBC, CFB, OFB).
  • Sec 4.6    Breaking DES (brief discussion).
  • Sec 4.8    Password security.  One way hash functions

• Chap 5:  The Advanced Encryption Standard (AES)

  • Sec 5.1    The basic algorithm (brief discussion, time permitting)

  • Sec 5.2    The layers of the algorithm (brief discussion, time permitting)

• Chap 6:  The RSA Algorithm

  • Sec 6.1    The RSA Algorithm.
  • Sec 6.2    Attacks on the RSA (brief discussion).
  • Sec 6.3    Primality testing.  The Rabin-Miller test.  
  • Sec 6.4    Progress in factoring large integers (brief discussion).
  • Sec 6.7    The public key concept.

• Chap 7:  Discrete Logarithms

  • Sec 7.1     Discrete logarithms.
  • Sec 7.3     Bit commitment.
  • Sec 7.4     The Diffie-Hellman key exchange algorithm.
  • Sec 7.5     The ElGamal public key cryptosystem.

• Chap 8:  Hash Functions

  • Sec 8.1     One-way hash functions.
  • Sec 8.3     The secure hash algorithm (SHA-1 and SHA-2).

• Chap 9:   Digital Signatures

  • Sec 9.1     RSA signatures.
  • Sec 9.2     El Gamal signature
  • Sec 9.3     Hashing and signing.

• Chaps 10--14

  • If time permits, a few selected topics from these sections will be covered

  Chap 18:  Error Correcting Codes

  • Sec 18.1   Introduction, examples of simple error-detecting and error-correcting codes.
  • Sec 18.2   Error-correcting codes, basic concepts and definitions, encoding and decoding.
  • Sec 18.3   Bounds on general codes.
  • Sec 18.4   Linear codes, syndrome decoding, the dual code.
  • Sec 18.5   Hamming codes.
  • Sec 18.7   Cyclic codes.
  • Sec 18.8   BCH codes (brief discussion, if time permits).
  • Sec 18.9    Reed-Solomon codes (brief discussion, if time permits).