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DICG (digital inversive congruential generator)

• Definition:
  

  y_n = a * inv(y_{n-1}) + b (mod p)      n > 0
  

  All operations are in the field F_{2^k} !!

• Name (as given to prng_new): "dicg(k,a,b,y_0)".
• Properties:
  • Period length = 2^k.
  • Strong non-linear properties.
  • Parameters seem not to be sensitive
  • prng_is_congruential is TRUE.
  • prng_can_seed is TRUE. The parameter of prng_seed will be used as y_{n-1} in the next call to get_next
• prng_can_fast_sub and prng_can_fast_con are FALSE.
• Parameter selection:

  Tricky.

• Introduced in:

  Eichenauer-Herrmann and Niederreiter, "Digital inversive pseudorandom numbers", ACM Transactions on Modeling and Computer Simulation, 4:339-349 (1994)