Random Numbers

Uses

• Gambling
• Simulation (especially digital hardware to generate stimuli)
• Encryption (uses random numbers for temporary private keys for communication)
• Ethernet (multiple devices trying to talk on same wire)

Definition

Value of each random number has no statistical correlation to any previous random variable

Two Types

• True Random
  • Flip coin infinite number of times and you can get an uncorrelated sequence
  • Ex: Thermal noise, solar radiation
• Pseudorandom
  • Seedable list of random numbers or generation of numbers in a procedural way
  • Provides numbers that when taken together have no correlation
  • Ex: Can generate using a linear shift feedback register that is multiplexed into itself

True Random Numbers

• Generated as needed from random natural phenomena
  • Atmospheric noise
  • Timing of radioactive decay
  • Timing of cosmic radiation event
  • Other stochastic process
• Hard to get right in hardware

Pseudorandom

• Easy to generate on demand

  • Fixed list of true random numbers
  • Algorithmically generated numbers with apparent local randomness

• Not truly random

  • Lists
    • Eventually run out
    • Stored somewhere
  • Generated values
    • Eventually repeat
    • Subject to modelling attacks

Use of Random Numbers

• Highest security, low refresh need: True Random
  • Cryptographic key generation
  • Lottery numbers
• Less security, high refresh or repeatability need: Pseudorandom
  • System modeling/simulation
• Hybrid Solution: moderate security: True random "seed"
  • Use random numbers to index into/initialize pseudorandom sequence