Cryptography 1000-135KRG
Basic cryptographic notions, classical cryptographic systems. Ciphers of Cesar, Viegenere, Playfair, and Hill. Cryptoanalysis of the classic ciphers.Statisical analysis, Friedman index of coincidence. Examples of other cryptographic systems: DES, AES. (2-3 lectures)
Computational complexity of group operation, Euclid algorithm and fast computation of modular powers (1 lecture)
Public key cryptosystems. Knapsac cryptographic system and the corresponding cryptoanalysis. LLL algorithm and applications. RSA, Diffie-Hellman, El Gamal and Massey -Omura cryptosystems. Digital signature standard. Provable security of cryptographic system. Hard computational problems. Factoring problem and discrete logarithm problem. (5-6 lectures)
Finite fields, generators of multiplicative group of the finite field. Factoring and discrete logarithm algorithms. Quadratic sieve, factor bases and Pollard's methods. Primality testing. Miller-Rabin and Solovay-Strassen tests. Zero knowledge protocols. (2-3 lectures)
Elliptic curves. Elliptic curves cryptosystems. Discrete logarithm problem on elliptic curve. Elliptic curve based factoring algorithm. (1-2 lectures)
Type of course
Learning outcomes
Knowledge and skills
A. Knowledge and understanding of:
- cryptographic primitives (definitions and examples), and
understanding of the concept of provable security of cryptosystem
- storage and communication complexity of cryptographic protocols
- formulated propositions (theorems, statements, facts,
lemmas, applications, and examples) related to the reduction
between the selected computational problems and algorithms
solving such problems
- basic mathematical methods used in the study of computational
problems applied in the cryptography
B. Practical ability to use theorems and algorithms for the study of specific computational problems
C. Ability to make appropriate choice of cryptographic system dedicated to the protection and the credibility of information processed in the computer system in relation to:
-Design and analysis of symmetric cryptographic systems
-Design and analysis of asymmetric cryptographic systems
-Cipher cryptanalysis
-Selecting and appropriate application of mathematical methods for
cryptographic systems
Social competence:
-Understanding of how to use cryptographic systems in computer
science
-Understanding and awareness of potential security threats to
computer system in relation to existing and potential hacking
attacks
-Ability of accurate, precise, and consistent with the rules of logic
formulation of statements, understanding of the role of the
reduction of system’s security to a specific computational problem
Assessment criteria
final test
oral exam
Bibliography
N. Koblitz, A course in number theory and cryptography, Springer, New York, 1994
Additional information
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