Creating different hash functions for integers in Python?

For my implementation of the minhashing algorithm I need to make many random permutations of integers, which will be simulated by using random hash functions (as many as possible). Currently I use hash functions of the form:

h(x) = (a*x + b) % c

where a and b are randomly generated numbers, and c is a prime number bigger than the highest value of b. Anyways, the code runs way too slow and it is impossible to use more than 15 of such hash functions in reasonable running time. Can anyone recommend other ways of using random hash functions for integers in Python? In other posts I came across suggestions for using bitwise shuffling and an XOR operation, but I didn't fully understand how one should implement something like this (I'm relatively new to Python).