Duration: 21 weeks
Number of lectures per week: 3
End-of-year Examination: 3-hour end of year exam
Topics to be covered by Dr. Murphy. Still to be added.
Topics to be covered by Dr. Purser. This part of course 374 will probably begin in the third week of the Michaelmas term. Details will be announced later.
The security of computer-based information, stored or transmitted.
Threats: Modification, Masquerade, Leakage, Replay, Repudiation, Traffic analysis, etc.
Identification, Secure access management (handshakes), Biometrics, etc.
Secret keys versus secret algorithms.
Generation, storage and transmission of secret keys.
Other aspects: Steganography, Chaffing Winnowing, Threshold crypto, etc.
Standard attacks: Known plaintext/cyphertext; Chosen plaintext/cyphertext; Brute force.
Long messages, All-or-nothing transform.
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).
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, Rijndael
Encryption modes: ECB, CBC, CFB, etc.
Integrity checks: MACs
Statistical crypt-analysis, shift-and-correlate, etc.
For symmetric keys; as ideal cyphertext.
Random number generators: LCGs, LFBSRs and MLSs, BBS, de Bruin sequences, etc.
Tests for randomness: String lengths, Chi-square.
Concept and invention of public-key crypto (Ellis, Cocks)
(Certification of public keys)
Modular arithmetic: Fermat, Euler, primitivity, totient function
The discrete logarithm (DL) problem
Diffie-Hellman and RSA
Very large integers and their implications.
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, etc.
Other techniques: Knapsack, Lucas series, elliptic curves, finite quaternions, affine maps, etc.
Holding private keys securely.
SHA-1, square-mod, MDC, RIPE-MD, RIPE-160, etc.
Keyed hash functions
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, Number field sieve.
The DL problem, Coppersmith et al.
The course will atempt to cover most of the above topics, some obviously less thoroughly than others.
Sep 8, 2004