Lucas Sequences in Cryptography This is a short note on the practical usefulness of Lucas sequences in applied cryptography. A Lucas sequence is a sequence of integers characterized by two parameters, P and Q. In practice Q is always 1 and the sequence is taken modulo a large integer. Calculating an element of a Lucas sequence is very similar to exponentiation. It may be helpful to think of P as ...

Least primitive root of prime numbers Least prime primitive root of prime numbers Least base necessary to prove the primality of a number Introduction Results References Links Contact Introduction Let p be a prime number. Fermat's little theorem states that a^(p-1) mod p=1 (a hat (^) denotes exponentiation) for all integers a between 1 and p-1. A primitive root of p is a number r such that any ...