Pseudorandom generators are fundamental to many theoretical and applied aspects of computing. We show howto construct a pseudorandom generator from any oneway function. Since it is easy to construct a one-way function from a pseudorandom generator, this result shows that there is a pseudorandom generator iff there is a one-way function.

The notion of non-malleable cryptography, an extension of semantically secure cryptography, is defined. Informally, in the context of encryption the additional requirement is that given the ciphertext it is impossible to generate a different ciphertext so that the respective plaintexts are related. The same concept makes sense in the contexts of string commitment and zero-knowledge proofs of possession of knowledge. Non-malleable schemes for each of these three problems are presented. The schemes do not assume a trusted center; a user need not know anything about the number or identity of other system users. Our cryptosystem is the first proven to be secure against a strong type of chosen ciphertext attack proposed by Rackoff and Simon, in which the attacker knows the ciphertext she wishes to break and can query the decryption oracle on any ciphertext other than the target.

A new public key cryptosystem is proposed and analyzed. The scheme is quite practical, and is provably secure against adaptive chosen ciphertext attack under standard intractability assumptions. There appears to be no previous cryptosystem in the literature that enjoys both of these properties simultaneously.

We describe an RSA-based signing scheme called PSS which combines essentially optimal efficiency with attractive security properties. Signing takes one RSA decryption plus some hashing, verification takes one RSA encryption plus some hashing, and the size of the signature is the size of the modulus. Assuming the underlying hash functions are ideal, our schemes are not only provably secure, but are so in a tight way — an ability to forge signatures with a certain amount of computational resources implies the ability to invert RSA (on the same size modulus) with about the same computational effort. Furthermore, we provide a second scheme which maintains all of the above features and in addition provides message recovery. These ideas extend to provide schemes for Rabin signatures with analogous properties; in particular their security can be tightly related to the hardness of factoring.

Since the appearance of public-key cryptography in the seminal Diffie-Hellman paper, many new schemes have been proposed and many have been broken. Thus, the

We show how to construct a public-key cryptosystem (as originally defined by Diffie and Hellman) secure against chosen ciphertext attacks, given a public-key cryptosystem secure against passive eavesdropping and a non-interactive zero-knowledge proof system in the shared string model. No such secure cryptosystems were known before. Key words. cryptography, randomized algorithms AMS subject classifications. 68M10, 68Q20, 68Q22, 68R05, 68R10 A preliminary version of this paper appeared in the Proc. of the Twenty Second ACM Symposium of Theory of Computing. y Incumbent of the Morris and Rose Goldman Career Development Chair, Dept. of Applied Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel. Work performed while at the IBM Almaden Research Center. Research supported by an Alon Fellowship and a grant from the Israel Science Foundation administered by the Israeli Academy of Sciences. E-mail: naor@wisdom.weizmann.ac.il. z IBM Research Division, T.J ...

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The prospect of a world in which all text, audio, picture, and video documents are in digital form on easily modifiable media raises the issue of how to certify when a document was created or last changed. The problem is to time-stamp the data, not the medium. We propose computationally practical procedures for digital time-stamping of such documents so that it is infeasible for a user either to back-date or to forward-date his document, even with the collusion of a time-stamping service. Our procedures maintain complete privacy of the documents themselves, and require no record-keeping by the time-stamping service. Appeared, with minor editorial changes, in Journal of Cryptology, Vol. 3, No. 2, pp. 99--111, 1991. 0 Time's glory is to calm contending kings, To unmask falsehood, and bring truth to light, To stamp the seal of time in aged things, To wake the morn, and sentinel the night, To wrong the wronger till he render right. The Rape of Lucrece, l. 941 1 Introduction ...

Much research in theoretical cryptography has been centered around finding the weakest possible cryptographic assumptions required to implement major primitives. Ever since Diffie and Hellman first suggested that modern

A new public key encryption scheme, along with several variants, is proposed and analyzed. The scheme and its variants are quite practical, and are proved secure against adaptive chosen ciphertext attack under standard intractability assumptions. These appear to be the first public-key encryption schemes in the literature that are simultaneously practical and provably secure.