Počet kreditů 6
Vyučováno v Summer
Rozsah výuky 4P+2S
Garant předmětu
Přednášející
Cvičící

The lecture will set mathematical foundations of modern cryptography (RSA, El-Gamal, elliptic curve cryptography, hashing). Also, the related algorithms for primality testing (numbers sieves) and discrete logarithms will be treated.

1. Basic notions of number theory, generators of random numbers and random primes.

2. A review of basic cryptosystems (RSA, El-Gamal).

3. Rabin-Miller test for generating random primes.

4. Using Euler's totient function for factorisation, generator of Z_m^*.

5. Hashing and message authentication.

6. Subexponential algorithms for factorisation and discrete logarithm.

7. Basic ideas of quadratic sieve.

8. Basic ideas of deterministic primality test.

9. Elliptic curves and their Abelian group.

10. Discrete logarithm on an elliptic curve. Generators of random elliptic curves.

11. Attacks on RSA cryptosytem and its implementation.

12. Quantum computing and satefy of cryptosystems.

13. Stockpile.

[1] D.Hankerson, A.J.Menezes, S.Vanstone, Guide to elliptic curve cryptography, Springer, 2004.

[2] V.Shoup, A Computational introduction to number theory and algebra, Cambridge University Press, 2008, http://shoup.net/ntb/

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