fast exponentiation in python

1def fast_exp(b, e, m): # Calculate b^e mod m
2    init = 2
3    powers = [b]
4    # Calculate b powers until e
5    while init <= e:
6        powers.append((powers[-1]**2) % m)
7        init *= 2
8    binary = bin(e)[2:][::-1]
9    product = 1
10    # We can now multiply the correct powers
11    for i in range(len(binary)):
12        if binary[i] == '1':
13            product *= powers[i]
14            product %= m
15    return product