It is impossible to discuss all the above applications of number theory.We only concentrate ourselves on the applications of nuber theory in com-puting. In the pas few decades,number theory has been successfully appliedto the following computing-related areas:

(1) Computer architecture and hardware design,

(2) Computcr soft ware systems design,

(3) Computer and network security.

(4) Random murnber generation

,5) Digital signal processing;

(6) Computer graphics and image processing.

(7) Error detection and correction.

(8 Faulty-tolerant computing,

(9y Algorithm analysis and design,

( 10) Theory of Computation, and

( 1l) Secure conputation andl communications.