Abstract:
The paper describes some elements of the
number theory and shows how they are used in modern information
security systems. As examples, the most famous protocols and
algorithms such as the Diffie-Hellman Protocol for pair key
generation, RSA and El Gamal public key encryption algorithms.
The generalized Euclid algorithm is considered, as a one of the
most common element of the number theory used in cryptography.
Algorithms are given RSA and El Gamal signature algorithms are
given. In conclusion,
the algorithm of the electronic signature based on
bilinear transformation uses a simplified case of the pairing
in the explicit law of reciprocity.