# 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
**Lecturer**- 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.

Time-stamping.

Trusted third parties (TTPs).

Anonymity**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**- None
**Assessment Detail**-
This module will be examined in a 2 hour
**examination**in Trinity term. Supplementals exams if required will consist of 100% exam.