Finding Inverse Modulo

LilLee

8/21/24, 4:35 AM

I'm working on a challenge like this:

def weird_func(FLAG)
    enc_flag = [(a + b*i) % n for i in FLAG]
    return bytes(enc_flag).hex()

Although I know the FLAG prefix which is flag{, without knowing a,b and n, I find it hard to calculate the whole FLAG. Only enc_flag is given in hex. I tried to brute-force but it seems like n is too large, or maybe I'm wrong. Can anyone help me step-by-step with this problem?

0 + 5

DannyNiu

8/21/24, 5:21 AM

Hint: $a + b \cdot i$ is a linear expression with 2 variables, with 2 of them, you have a system of equations enough to solve it. You may be already familiar with it in real numbers, now you just do it modulo $n$. (If $n$ is a prime, then it's a field just like real numbers).

poncho

8/21/24, 3:16 PM

What control do you have over FLAG? Can you arbitrarily set the prefix? Or, do you know the prefix but can't set it?

LilLee

8/21/24, 3:57 PM

@poncho well I just guess that the FLAG will be in the same format as before, so I'm assuming that I know the first 5 characters, `flag{`. I'm not familiar with this so finding `n` is tough to me.

fgrieu

8/21/24, 4:11 PM

@LilLee: assuming your code needs only an additional `:` to be executable with `FLAG` on the tune of `b"flag{"`, we can find a very likely maximum value for `n`, and it's not large. And you (not us) can find a minimum, further narrowing down the values of `n`. Then the first hint applies.

aiootp

8/21/24, 4:43 PM

Hint: In python, given `c = (b * i) % n`, then `b_inverse = pow(b, n - 2, n)`, and `i == (b_inverse * c) % n`

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: Finding Inverse Modulo

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