Create a random permutation of 1..N in constant space

Question

I am looking to enumerate a random permutation of the numbers 1..N in fixed space. This means that I cannot store all numbers in a list. The reason for that is that N can be

Answer 1

Here's some SageMath code that should generate a random permutation the way Daniel Fischer suggested:

def random_safe_prime(lbound):
    while True:
        q = random_prime(lbound, lbound=lbound // 2)
        p = 2 * q + 1
        if is_prime(p):
            return p, q


def random_permutation(n):
    p, q = random_safe_prime(n + 2)

    while True:
        r = randint(2, p - 1)
        if pow(r, 2, p) != 1 and pow(r, q, p) != 1:
            i = 1
            while True:
                x = pow(r, i, p)
                if x == 1:
                    return

                if 0 <= x - 2 < n:
                    yield x - 2

                i += 1