Seeking prime numbers quickly through parallel-computing

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Seeking prime numbers quickly through
parallel-computing

• Daniel J. Wright

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Seeking prime numbers quickly through
parallel-computing

• Reasoning / Background
• Project Goals
• Methodology and Assumptions
• Software Description
• Result Data
• Conclusions

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Reasoning / Background

• DES U.S. Government Data Encryption Standard
  72,057,594,037,927,936 (72 quadrillion) possible
  keys.
• Cracked by the Electronic Frontier Foundations
  Deep Crack software and hardware in just over
  22 hours, trying 245 billion keys per second.
• How?

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Parallel Processing!!!

• Multiple CPUs networked together and assigned
  only a portion of the entire work to be completed.

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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?

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Parallel Processing!!!

• Multiple CPUs networked together to find very
  large prime numbers faster than any one machine
  could.

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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.

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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.

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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.

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Software Description

• 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.

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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.

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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.

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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.

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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.

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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.

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Results

• Standalone Version - Pentium 100

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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 !

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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 !

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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.

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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.

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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

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