Pseudorandom Number Generation Programming

1
Pseudorandom Number Generation Programming

• Jonas Tan
• jonastan_at_cs.tamu.edu

2
True Random Number

• Almost true sources of random numbers come from
  physical means, they tend to be either costly or
  slow.
• Coin Tossing
• Radiation pulse

3
Requirement for Generating Pseudorandom Number

• Randomness
• Uniform distribution
• Independence
• Unpredictability
• The next random number cannot be predicted by
  inspecting the generated number sequence.

4
A Cryptographically Generated Random Number
Generator

• Meyer, C., and Matya, S. Cryptography A new
  Dimension in Computer Data Security. New York
  Wiley, 1982
• Take advantage of the encryption logic available
  to produce random numbers.
• DES key and the seed C must be kept secretly.
• If 56-bit DES key is produced, then a counter
  with period 256 can be used.

5
A Cryptographically Generated Random Number
Generator
We adopt DES in our program.
6
A Cryptographically Generated Random Number
Generator

• Each of the outputs X0, X1,,Xn-1 is based on
  different counter value and therefore
  X0!X1!!Xn-1

7
Program Exercise

• Open \2000SummerProject\NumberTheoryUI\2006Main.sl
  n
• Open project Random
• Add your codes into random.cs
• BigInteger RandomNumber(BigInteger C, int len)
• //Generate a random number of len64-bit length
• BigInteger r
• uint tmp new uintlen2
• for i0 to n step 2
• use DES function DES.DesEncrypt to get a long
  integer xi
• separate xi into two uint (use shift)
• //initial r by tmp
• Return r