THE ITERATED CARMICHAEL λ-FUNCTION AND THE NUMBER OF CYCLES OF THE POWER GENERATOR GREG MARTIN AND CARL POMERANCE

@inproceedings{Pomerance2005THEIC,
  title={THE ITERATED CARMICHAEL λ-FUNCTION AND THE NUMBER OF CYCLES OF THE POWER GENERATOR GREG MARTIN AND CARL POMERANCE},
  author={Carl Pomerance},
  year={2005}
}
A common pseudorandom number generator is the power generator: x 7→ x (mod n). Here, `, n are fixed integers at least 2, and one constructs a pseudorandom sequence by starting at some residue mod n and iterating this `th power map. (Because it is the easiest to compute, one often takes ` = 2; this case is known as the BBS generator, for Blum, Blum, and Shub.) To be a good generator, the period should be large. Of course, the period depends somewhat on the number chosen for the initial value… CONTINUE READING

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