"The Simplest Protocol for Oblivious Transfer" Revisited

In 2015, Chou and Orlandi presented an oblivious transfer protocol that already drew a lot of attention both from theorists and practitioners due to its extreme simplicity and high efficiency. Chou and Orlandi claimed that their protocol is UC-secure in the random oracle model under dynamic corruptions, which is a very strong security guarantee. Unfortunately, in this work we point out a flaw in their security proof for the case of sender corruption. We define a decisional problem and we prove that, if a correct proof is provided, then this problem can be solved correctly with overwhelming probability. Therefore, the protocol by Chou and Orlandi cannot be instantiated securely with groups for which our decisional problem cannot be solved correctly with overwhelming probability. Our decisional problem can be solved with overwhelming probability when a DDH oracle is provided. Therefore, it seems likely that the protocol by Chou and Orlandi can be instantiated securely with gap-DH groups.