Probabilistic encryption

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Abstract

A new probabilistic model of data encryption is introduced. For this model, under suitable complexity assumptions, it is proved that extracting any information about the cleartext from the cyphertext is hard on the average for an adversary with polynomially bounded computational resources. The proof holds for any message space with any probability distribution. The first implementation of this model is presented. The security of this implementation is proved under the interactability assumptin of deciding Quadratic Residuosity modulo composite numbers whose factorization is unknown.

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This research was done when both authors were students at the University of California at Berkeley and supported in part by NSF Grant MCS 82-04506. The preparation of this manuscript was done when the first author was at the Laboratory of Computer Science at MIT and supported by a Bantrell fellowship and an IBM faculty development award, and the second author was at the Computer Science Department at the University of Toronto.