| In this thesis we present the elements of factoring multiple-precision integers, implemented in the C programming language. We investigate two methods of factorization, Fermat factorization and Pollard's rho method. We explore the Chinese Remainder Theorem to understand how modular arithmetic is used, and relate this to the utilization of threads in parallel processing for factorization, and further relate these to operating systems threading principles to demonstrate the advantageous utilization of concurrent threads. In particular we utilize the Portable Operating Systems Interface for Unix (POSIX) pthreads Application Programming Interface (API) to illustrate parallel processing and thread control, which are applicable to the factorization of multiple-precision integers. We finally relate these computational methods developed to encryption and decryption processes involved in Rivest-Shamir-Adleman (RSA) cryptography. |
