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We introduce the notion of multi-trapdoor commitments which is a stronger form of trapdoor commitment schemes. We then construct two very ecien t instantiations of multi-trapdoor commitment schemes, one based on the Strong RSA Assumption and the other on the Strong Die-Hellman Assumption. The main application of our new notion is the construction of a compiler that takes any proof of knowledge and transforms it into one which is secure against a concurrent man-in-the-middle attack (in the common reference string model). When using our specic implementations, this compiler is very ecien t (requires no more than four exponentiations) and maintains the round complexity of the original proof of knowledge. The main practical applications of our results are concurrently secure identication protocols. For these applications our results are the rst simple and ecien t solutions based on the Strong RSA or Die-Hellman Assumption.

Multi-trapdoor Commitments and Their Applications to Proofs of Knowledge Secure Under Concurrent Man-in-the-Middle Attacks