Nonce reuse. Due to rising entropy prices, Roseacrucis has started to reuse nonces. You must perform the Forbidden Attack in order to recover the authentication key and forge arbitrary ciphertext.
Recall that the AES-GCM ciphertext is computed as the XOR of the keystream and the message. One can modify the bits of the ciphertext arbitrarily to effect the same change in the decrypted plaintext.
Where certain bits of the plaintext are already known, the attacker can fully determine the same bits of the forged plaintext. If nonces are reused, the keystream will be identical, allowing us to recover plaintext via crib dragging, which makes this attack particularly effective.
However, we still need to compute a new MAC over the forged ciphertext. Simplifying for a ciphertext \(c\) of two blocks, the GMAC MAC is computed as \[ mac = s + (len)h + c_1h^2 + c_0h^3, \] where \(s\) is a constant depending on the AES-GCM key and the nonce, and \(h\) is the authentication key depending only on the AES-GCM key.
If we intercept a second ciphertext \(c'\) encrypted under the same key and nonce, we can compute \[ mac + mac' = (s + s') + (len + len')h + (c_1 + c'_1)h^2 + (c_0+c'_0)h^3, \] Since \(s = s'\) and \(x+x=0 \in \mathbb{F}_{2^{128}}\), we are left with the polynomial equation \[ 0 = (mac + mac') + (len + len')h + (c_1 + c'_1)h^2 + (c_0+c'_0)h^3 \] where all variables are known other than \(h\). Thus, recovering \(h\) is a simple matter of finding the roots by factoring the polynomial using a computer algebra system such as SageMath.
We plug \(h\) back into the first equation to recover \(s\), and finally, we can forge the MAC for arbitary ciphertext under the same nonce.
from aesgcmanalysis import xor, gcm_encrypt, nonce_reuse_recover_secrets, forge_gmac k = b"YELLOW_SUBMARINE" nonce = b"JORGELBORGES" m1 = b"""The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings.""" aad1 = b"The Anatomy of Melancholy" m2 = b"From any of the hexagons one can see, interminably, the upper and lower floors." aad2 = b"Letizia Alvarez de Toledo" c1, mac1 = gcm_encrypt(k, nonce, m1, aad1) c2, mac2 = gcm_encrypt(k, nonce, m2, aad2) # Recover the authentication key and blind from public information h, s = nonce_reuse_recover_secrets(nonce, aad1, aad2, c1, c2, mac1, mac2) # Forge the ciphertext m_forged = b"As was natural, this inordinate hope was followed by an excessive depression." c_forged = xor(c2, xor(m2, m_forged)) aad_forged = b"You who read me, are You sure of understanding my language?" mac_forged = forge_gmac(nonce, h, s, c_forged, aad_forged) assert gcm_decrypt(k, nonce, c_forged, aad_forged, mac_forged) == m_forged