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Module MA346A: Cryptology

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas Term 2013-14
Contact Hours
11 weeks, 3 lectures including tutorials per week
Dr. Michael Purser
Learning Outcomes
Module Content
  • Introduction
  • The security of computer-based information, stored or transmitted.
    Threats: Modification, Masquerade, Leakage, Replay, Repudiation, Traffic analysis, etc.
    Services: Confidentiality (message, traffic),
    Authenticity (Integrity, Proof and Non-repudiation of Origin or Reception or Delivery, etc.)
    Identification: What you know, what you have, what you are.
    Secure access management (handshakes), Biometrics.
    Secret keys versus secret algorithms.
    Generation, storage and transmission of secret keys.
    Examples:  Symmetric encryption: Caesar’s cypher
    Integrity: CRC/Hash
    Authentication: Keyed hash, DES MAC
    Other aspects: Steganography, Threshold crypto.
    Standard attacks: Known plaintext/cyphertext; Chosen plaintext/cyphertext; Brute force.
    Long messages, All-or-nothing transform.

  • Concepts
  • Shannon’s theories: Unicity key lengths and distances, Perfect secrecy.
    Symmetric key cryptography: Encryption and MACs (message authentication checks).
    Asymmetric Key cryptography: Encryption and digital signatures.
    Distribution and certification of public keys.
    Trusted third parties (TTPs).

  • Symmetric or Secret Key Cryptology
  • History: Substitution, permutation, involution.
    Vigenere, Beaufort, Polyalphabetic, Jefferson Wheel, Wheatstone Disc, Enigma
    DES (Data encryption standard), Triple-DES, IDEA etc.
    The AES Project: Mars, Twofish, RC6, Serpent
    The winner Rijndael
    Encryption modes: ECB, CBC, CFB, etc.
    Integrity checks: MACs
    Stream cyphers.
    Statistical crypt-analysis, shift-and-correlate.

  • Random numbers and sequences
  • For symmetric keys; as ideal cyphertext.
    Random number generators: LCGs, LFBSRs and MLSs, BBS, de Bruin sequences.
    Tests for randomness: String lengths, Chi-square.

  • Asymmetric Public Key Cryptography
  • Concept and invention of public-key crypto (Ellis, Cocks)
    Certification of public keys
    Bi-prime crypto
    Modular arithmetic: Fermat, Euler, primitivity, totient function
    The discrete logarithm (DL) problem
    Diffie-Hellman and RSA
    Rabin encryption
    Very large integers and their implications.


  • Asymmetric system techniques
  • RSA parameters and frustrating attacks.
    Primality testing: Rabin, Carmichael numbers
    RSA security: order of the group.
    Modular inverses, Euclid, continued fractions.
    Chinese remainder theorem (CRT)
    Speeding up the arithmetic: Karatsuba, Montgomery, small exponents.
    Other algorithms: DSA/SHA-1 signature standard.
    RPK, MTI/A0, MTI/C0, MQV, Quadratic residues, Fiat-Shamir, Elgamal
    Other techniques: Knapsack, Lucas series, elliptic curves, finite quaternions, affine maps
    Holding private keys securely.

  • Hash functions
  • Desiderata
    SHA-1, square-mod, MDC, RIPE-MD, RIPE-160
    The competition for replacing SHA
    Keyed hash functions

  • More crypt-analysis
  • Differential crypt-analysis (Bihar-Shamir)
    Linear crypt-analysis (Matsui)
    Factorising: Fermat, the birthday paradox and Pollard Monte Carlo, Pollard (p+1).
    Sub-exponential complexity and the use of factor bases:
    Dixon’s method, Quadratic sieve, Continued fractions, Introduction to the Number Field Sieve.
    The DL problem, Coppersmith et al.

    Module Prerequisite
    Assessment Detail
    This module will be examined in a 2 hour examination in Trinity term. Supplementals exams if required will consist of 100% exam.