Everything is still Big

Same problem as the previous similar name challenge. But there is a twist this time. There is a check of (3*d)**4 > N, which effectively renders Weiner's attack useless.

We can use Boneh-Durfee Attack. Awesome script at this link. The Github repo contains some useful scripts.

Boneh-Durfee Attack limit:

d < N^{0.292}

From the retrieved d, we can easily recover the plaintext.

Seems like there is another solution by aloof, which I am too lazy to type so here's the screenshot of the math involved.

Sage Implementation:


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N = ...
e = ...
c = ...
s = floor(sqrt(N))
M = Matrix([[e, s], [N, 0]])
Mred = M.LLL()
D = [abs(Mred[i, 1]) // s for i in [0,1]]

for d in D:
    t = randint(2, N - 2)
    tt = pow(t, e, N)
    if tt^d != t:
        continue
    flag = int(pow(c, d, N))
    flag = flag.to_bytes((flag.bit_length() + 7)//8, 'big')
    print(f'FLAG: {flag.decode()}')