We argue that the random oracle model -- where all parties have access to a public random oracle -- provides a bridge between cryptographic theory and cryptographic practice. In the paradigm we suggest, a practical protocol P is produced by first devising and proving correct a protocol P R for the random oracle model, and then replacing oracle accesses by the computation of an "appropriately chosen" function h. This paradigm yields protocols much more efficient than standard ones while retaining many of the advantages of provable security. We illustrate these gains for problems including encryption, signatures, and zero-knowledge proofs.

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.

Publicly accessible databases are an indispensable resource for retrieving up to date information. But they also pose a significant risk to the privacy of the user, since a curious database operator can follow the user's queries and infer what the user is after. Indeed, in cases where the users ' intentions are to be kept secret, users are often cautious about accessing the database. It can be shown that when accessing a single database, to completely guarantee the privacy of the user, the whole database should be downloaded, namely n bits should be communicated (where n is the number of bits in the database). In this work, we investigate whether by replicating the database, more efficient solutions to the private retrieval problem can be obtained. We describe schemes that enable a user to access k replicated copies of a database (k * 2) and privately retrieve information stored in the database. This means that each individual database gets no information on the identity of the item retrieved by the user. Our schemes use the replication to gain substantial saving. In particular, we have ffl A two database scheme with communication complexity of O(n1=3). ffl A scheme for a constant number, k, of databases with communication complexity O(n1=k). ffl A scheme for 13 log2 n databases with polylogarithmic (in n) communication complexity.

We present general definitions of security for multi-party cryptographic protocols, with focus on the task of evaluating a probabilistic function of the parties' inputs. We show that, with respect to these definitions, security is preserved under a natural composition operation. The definitions follow the general paradigm of known definitions; yet some substantial modifications and simplifications are introduced. The composition operation is the natural `subroutine substitution' operation, formalized by Micali and Rogaway. We consider several standard settings for multi-party protocols, including the cases of eavesdropping, Byzantine, non-adaptive and adaptive adversaries, as well as the information-theoretic and the computational models. In particular, in the computational model we provide the first definition of security of protocols that is shown to be preserved under composition.

We define a Universal One-Way Hash Function family, a new primitive which enables the compression of elements in the function domain. The main property of this primitive is that given an element x in the domain, it is computationally hard to find a different domain element which collides with x. We prove constructively that universal one-way hash functions exist if any 1-1 one-way functions exist. Among the various applications of the primitive is a One-Way based Secure Digital Signature Scheme which is existentially secure against adoptive attacks. Previously, all provably secure signature schemes were based on the stronger mathematical assumption that trapdoor one-way functions exist. Key words. cryptography, randomized algorithms AMS subject classifications. 68M10, 68Q20, 68Q22, 68R05, 68R10 Part of this work was done while the authors were at the IBM Almaden Research Center. The first author was supported in part by NSF grant CCR-88 13632. A preliminary version of this work app...

In this paper we prove the intractability of learning several classes of Boolean functions in the distribution-free model (also called the Probably Approximately Correct or PAC model) of learning from examples. These results are representation independent, in that they hold regardless of the syntactic form in which the learner chooses to represent its hypotheses. Our methods reduce the problems of cracking a number of well-known public-key cryptosystems to the learning problems. We prove that a polynomial-time learning algorithm for Boolean formulae, deterministic finite automata or constant-depth threshold circuits would have dramatic consequences for cryptography and number theory: in particular, such an algorithm could be used to break the RSA cryptosystem, factor Blum integers (composite numbers equivalent to 3 modulo 4), and detect quadratic residues. The results hold even if the learning algorithm is only required to obtain a slight advantage in prediction over random guessing. The techniques used demonstrate an interesting duality between learning and cryptography. We also apply our results to obtain strong intractability results for approximating a generalization of graph coloring.

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 ...

Abstract not found

We show how a pseudo-random generator can provide a bit commitment protocol. We also analyze the number of bits communicated when parties commit to many bits simultaneously, and show that the assumption of the existence of pseudo-random generators suffices to assure amortized O(1) bits of communication per bit commitment.

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 ...