Cryptography and Information Security

The main aim of the lecture is introduction to cryptographic methods and information security in computer systems, computer networks and telecommunications. Ciphers, cryptographic protocols, private and public key cryptography, digital signatures and hash functions are main stream of the lecture. Special attention is paid to mathematical aspects of presented methods.

Lecture contents

1. Short introduction to cryptography and data security (2h): cryptographic objectives and primitives, overview of data
   security problems, alphabet, language, codes, ciphers, private key
   ciphers, public key ciphers, block ciphers, stream ciphers, product
   ciphers, one way functions, permutation ciphers, substitution ciphers,
   homophonic substitution ciphers, polyalphabetic substitution ciphers,
   classical ciphers (linear and affine ciphers, Hill cipher, Caesar
   cipher, Playfair cipher, Vigenere cipher, Enigma), ideal ciphers
   (Vernam cipher), ciphers and information theory approach, Shannon
   theorem.


2. Mathematical methods in cryptography (4h): divisibility,
   congruencies, Euler`s theorem, GCD and extended Euclid`s algorithm,
   Chinese Remainder Theorem, abstract algebra, group theory, discrete
   logarithm, commutative rings and fields, elliptic curves, point
   lattices, computational complexity and NP hard problems (integer
   factorization problem, discrete logarithm problem, Diffi-Hellmann
   problem).


3. Public key ciphers (4h): RSA, ElGamal, Rabin, Massey-Omura
   cipher, probabilistic PK ciphers, elliptic curve based ciphers, point
   lattice based ciphers, Mc Eliece and correcting codes based ciphers,
   knapsack public key ciphers, generation of public key cipher
   parameters.


4. Private key ciphers(4h): permutation-substitution networks,
   avalanche effect, Feistel cipher, round, S-boxes, general private key
   cipher structures, DES, 3DES, DESX, AES, IDEA, FEAL, Twofish, Blowfish,
   MARS, CAST 256, SAFER, Serpent, Camelia, RC5, RC6, TEA.


5. Stream ciphers and ciphering modes (2h): stream ciphers based on LFSRs, RC4 stream cipher, ECB, CBC, OFB, CFB.


6. Hash functions and data integrity (2h): properties and
   classification of hash functions, relationships between the
   properties, MDC and MAC hash functions, MD5, SHA-1, Whirlpool,
   Chaum-van Heijst-Pfitzmann hash functions, hash functions based on
   block ciphers (Rabin method, Davis method, Matyas-Meyer-Oseas method),
   birthday paradox and cryptanalysis of hash functions.


7. Document authentication (digital signatures) (2h): basic digital signatures properties, different kinds of digital signatures, one time signatures, RSA signatures, ElGamal signatures (classical and on groups), DSA standard, Schnorr signatures, blind signatures, undeniable signatures, fail-stop signatures.


8. Entity authentication (identification) (2h): password methods (weak authentication), challenge-response methods (strong
   authentication), zero knowledge algorithms, Fiat-Shamir algorithm,
   Feige-Fiat-Shamir algorithm, Guillou-Quisquater algorithm, digital
   signatures based on zero knowledge authentication algorithms.


9. Secret sharing (1h): trivial secret sharing, Shamir scheme,
   Blakley scheme, Chinese Remainder Theorem based secret sharing.


10. Effective implementation of cryptographic algorithms (1h): fast exponentiations algorithms, fast GCD computations, binary extended
    Euclid algorithm, fast algorithms for multiple-precision residual and
    integer arithmetic, Barrett algorithm, Mongomery algorithm, specialized
    hardware solutions.


11. Random and pseudorandom numbers generators for cryptographic aims (1h): true random number generators (TRNG) and pseudorandom number generators (PRNG), ANSI X9.17, FIPS 186 generator,
    Micalli-Schnorr generator, RSA generator, BBS generator.


12. Primality testing and prime numbers generators (1h): probabilistic and deterministic primality tests, Erastotenes sieve, Solovay-Strassen algorithm, Miller-Rabin algorithm, deterministic tests, AKS primality test


13. Key distribution algorithms and protocols (1h): Diffi-Hellman algorithm, TTP, Wide Mouth Frog Protocol, Needham-Schroeder protocol.


14. Key management (1h): Public Key Infrastructure (PKI) and
    Certificate Authority (CA).

• Classical ciphers and cryptanalysis of classical ciphers (2h): Caesar cipher, Vigenere cipher, Enigma, linear and affine ciphers.
  
• Congruencies (2h): properties of congruencies, set of
  congruencies, GCD and GCD complexity, Chinese Remainder Theorem and RNS
  (Residue Number System), quadratic residues.


• Abstract algebra (6h): basic properties of groups, multiplicative groups, rings and cyclic groups, discrete logarithms in cyclic groups, rings, finite fields, inverses in rings and finite fields, computations in finite fields and rings, Hamming distance and basic concepts of correcting codes, quotient rings and ideals


• Public key ciphers (2h): Examples of public key ciphers (RSA, ElGamal, Rabin) with small parameters


• Digital signatures (2h): Examples of digital signatures
  (RSA, ElGamal) with small parameters

1. A. Menezes, P. van Oorsschot, S. Vanstone, Handbook of Applied
   Cryptography, CRC Press, 2001.


2. J. Buchmann, Introduction to cryptography, Springer Verlag, 2007,
   Berlin, Heidelberg, 2007.


3. V. Shoup, A Computational Introduction to Number Theory and
   Algebra, Cambridge University Press, Cambridge, 2005.

There are 3 mid-term tests (during lectures). Maximum score for every
mid-term test is 20 points. For the project it is possible to score up
to 40 points. For the exam it is possible to score up to 100 points.
Additional extra points can be obtained for solving problems during
tutorials (2 points for one solved problem) and for homework (5 points
for one solved problem).

The final result is based on the following pattern:

5.0: 180-200 (or more) points

4.5: 160-179 points

4.0: 140-159 points

3.5: 120-139 points

3.0: 100-119 points

2.0: 0-99 points