Permutation binomials and their groups

This paper is devoted to studying properties of permutation binomials over finite fields and studying possibility to use permutation binomials as enryption function. We present permutation binomials enumeratation algorithm. Using this algorithm all permutation binomials for finite field up to order 15000 were generated. Using this data we investigate groups, generated by permutation binomials and found that over some finite fields $\mathbb F_q$ every bijective function over $[1..q-1]$ can be represented as composition of binomials. We study possibility of permutaion binomials generation over large prime fields. And we prooved that RSA generalization using permutation binomials isn't secure.