Symmetrical hyperbolic functionsand a cryptograpic application

A. Stakhov, B. Rozin defined symmetrical hyperbolic functions which are the being extensions of Binet formulas for the Fibonacci and Lucas numbers in continuous domain. By concidering the characteristical polynomial of the Fibonacci sequences, the sequences and for the characteristical polynomial , can be obtained with following reccurence relations , ; , and , ; , .In this thesis, the proporties of and , the relations between and , also the relations between hyperbolic functions and them were given. Furthermore, the symmetrical hyperbolic functions and were defined, which are continuous cases of and . By the help of these functions, Generalized Golden Matrices were defined. Finally, a cryptographic application were given, in which the Generalized Golden Matrices are used. Science Code : 204.1.025 Key Words : Symmetrical Hyperbolic Functions, cryptography Page number : 89 Adviser : Prof. Dr. Dursun TAŞÇI