Revisiting MAC Forgeries, Weak Keys and Provable Security of Galois/Counter Mode of Operation

Galois/Counter Mode (GCM) is a block cipher mode of operation widely adopted in many practical applications and standards, such as IEEE 802.1AE and IPsec. We demonstrate that to construct successful forgeries of GCM-like polynomial-based MAC schemes, hash collisions are not necessarily required and any polynomials could be used in the attacks, which removes the restrictions of attacks previously proposed by Procter and Cid. Based on these new discoveries on forgery attacks, we show that all subsets with no less than two authentication keys are weak key classes, if the final block cipher masking is computed additively. In addition, by utilizing a special structure of GCM, we turn these forgery attacks into birthday attacks, which will significantly increase their success probabilities. Furthermore, we provide a method to fix GCM in order to avoid the security proof flaw discovered by Iwata, Ohashi and Minematsu. By applying the method, the security bounds of GCM can be improved by a factor of around 2. Lastly, we show that these forgery attacks will still succeed if GCM adopts MAC-then-Enc paradigm to protect its MAC scheme as one of the options mentioned in previous papers.