Seeking prime numbers quickly through parallel-computing

1. Seeking prime numbers quickly through parallel-computing Daniel J. Wright

2. Seeking prime numbers quickly through parallel-computing • Reasoning / Background • Project Goals • Methodology and Assumptions • Software Description • Result Data • Conclusions

3. Reasoning / Background • DES: U.S. Government Data Encryption Standard: 72,057,594,037,927,936 (72 quadrillion) possible keys. • Cracked by the Electronic Frontier Foundation’s “Deep Crack” software and hardware in just over 22 hours, trying 245 billion keys per second. • How?

4. Parallel Processing!!! • Multiple CPU’s networked together and assigned only a portion of the entire work to be completed.

5. Reasoning / Background • RC5: Public key encryption • Two keys (one public and one private) are generated based on the factors of a third number. • Recipe for a hard-to-factor number: Multiply two very large prime numbers together. • How do we find large prime numbers quickly?

6. Parallel Processing!!! • Multiple CPU’s networked together to find very large prime numbers faster than any one machine could.

7. Project Goals • To develop software that utilizes multiple CPUs to solve a problem more quickly than any one of the CPUs alone. • To demonstrate a usage for legacy equipment. • To implement the software within a frame of three months.

8. Description • Two sets of software were written for comparison purposes. • Standalone version designed to find prime numbers very quickly. • Networked version designed to cooperate with multiple PCs to find the same range of prime numbers.

9. Methodologies and Assumptions • Finding prime numbers is not a hard task. • Fast prime number algorithms are not 100% effective. • The networked version uses identical algorithms for actually calculating the primes. • Both software versions are capable of benchmarking themselves.

10. Standalone Version: Accepts all project details on the command line. Uses the Rabin-Miller algorithm for finding prime numbers. Outputs resulting data to pre-designated output files. Networked Client: Accepts project details from the project server. Uses the Rabin-Miller algorithm for finding prime numbers. Sends resulting data back to the server. Software Description

11. Software Description • Networked Server: • Accepts project details from the command line. • Utilizes multiple threads to allow concurrent access of all of the clients at the same time. • Handles all data flow to and from the the clients with a central database object. • Outputs the results of all the clients work to pre-designated output files.

12. Software Description • Considerations: • The central database must be able to handle the critical section problem for an unlimited number of processes. • The central database must be able to intelligently assign blocks of numbers to each client so that all clients finish in the same amount of time. • The central database must operate efficiently.

13. Software Description • Central Database: • Wrapper object holding 6 separate object-oriented databases. • Project Information Database - Maintains overall status information regarding the rest of the databases. • Client Table - Maintains listing of all clients that are registered with the database along with current assignment and benchmark information.

14. Software Description • Central Database: (Continued) • Unassigned List, Assigned List, Done List, Prime List • Uses polymorphism to inherit the list class. • List Class: Contains the Unassigned Record, Assigned Record, Done Record and Prime Record which are all use polymorphism to inherit the record class.

15. Resources • Hardly Any! Project needed to demonstrate a positive usage for legacy equipment. • Developed with GCC on a Pentium 100 running Red Hat Linux 5.1. • Tested on multiple Linux work stations and legacy Sun Sparc Stations.

16. Results: • Standalone Version - Pentium 100

17. Results: • All primes between 1 and 25,000: • One system was able to process 260 numbers per second. • Two systems cooperating were able to process 454 numbers per second. • An increase of 75% !

18. Results: • All primes between 1 and 250,000: • One system was able to process 43 numbers per second. • Two systems were able to process 134 numbers per second. • An increase of 210% !

19. Results: • All primes between 1 and 250,000: • Some Sun Sparc Stations were unable to complete the project as a standalone system due to CPU time limits. • Other workstations that managed to complete the project processed an average of 25 numbers per second. • In a combined effort, 9 workstations were able to process 250,000 numbers at a rate of 200 numbers per second.

20. Conclusions: • Parallel processing improves processing speed. • Legacy systems can still be powerful machines if there are enough of them. • As ubiquitous computing becomes more prominent, the processing of data can not be limited by the capabilities of any one system.

21. For further information • Project documentation: • HTTP://www.pitt.edu/~djwst18/coursework • RSA Encryption • HTTP://www.rsa.com • Unix network programming • HTTP://www.interlog.com/~vic/sock-faq.html • Unix interprocess communication • HTTP://www.kohala.com/~rstevens