Polynomial-Time, Semantically-Secure Encryption Achieving the Secrecy Capacity

In the wiretap channel setting, one aims to get information-theoretic privacy of communicated data based only on the assumption that the channel from sender to adversary is noisier than the one from sender to receiver. The secrecy capacity is the optimal (highest possible) rate of a secure scheme, and the existence of schemes achieving it has been shown. For thirty years the ultimate and unreached goal has been to achieve this optimal rate with a scheme that is polynomial-time. (This means both encryption and decryption are proven polynomial time algorithms.) This paper finally delivers such a scheme. In fact it does more. Our scheme not only meets the classical notion of security from the wiretap literature, called MIS-R (mutual information security for random messages) but achieves the strictly stronger notion of semantic security, thus delivering more in terms of security without loss of rate. 1 Department of Computer Science & Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA. Email: [email protected]. URL: http://www.cs.ucsd.edu/users/mihir. Supported in part by NSF grants CNS-0904380 and CCF-0915675. 2 Department of Computer Science & Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA. Email: [email protected]. URL: http://www.cs.ucsd.edu/users/stessaro. Supported in part by Calit2 and NSF grant CNS-0716790.