Basic Montgomery ladder implementation. In the test it works with just numbers, but you can plug in any operation.

montgomery_ladder.py

#!/usr/bin/python3 -O

from math import floor, log

def montgomery_ladder(x, n, op, select):
    k = floor(log(n, 2)) + 1
    x1 = x
    x2 = op(x, x)
    for i in range(k - 2, -1, -1):
        bit = 1 if n & (1 << i) else 0
        q = select(bit, x2, x1)
        qq = op(q, q)
        x1x2 = op(x1, x2)
        x1 = select(bit, x1x2, qq)
        x2 = select(bit, qq, x1x2)
    return x1

def const_time_select(bit, a, b):
    mask = bit - 1
    return mask & b | ~mask & a

if __name__ == "__main__":
    import dis
    for instr in dis.Bytecode(const_time_select):
        assert not instr.is_jump_target
    
    for x in range(0, 10):
        for n in range(1, 10):
            assert montgomery_ladder(x, n, lambda a, b: a + b, const_time_select) == x*n
            assert montgomery_ladder(x, n, lambda a, b: a * b, const_time_select) == x**n
    print("self test passed")