Duration: 19 weeks
Number of lectures per week: 3
End-of-year Examination: 3-hour end of year exam
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.
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 The winner Rijndael
Encryption modes: ECB, CBC, CFB, etc.
Integrity checks: MACs
Statistical crypt-analysis, shift-and-correlate.
For symmetric keys; as ideal cyphertext.
Random number generators: LCGs, LFBSRs and MLSs, BBS, de Bruin sequences.
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.
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.
Desiderata SHA-1, square-mod, MDC, RIPE-MD, RIPE-160 The competition for replacing SHA 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, Introduction to the Number Field Sieve.
The DL problem, Coppersmith et al.
The course will attempt to cover most of the above topics, some obviously less thoroughly than others. The best guides to coverage are the exam papers of the last decade.
Lecture notes available at:
Feb 28, 2010