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.

We propose a fully functional identity-based encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational Diffie-Hellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic curves is an example of such a map. We give precise definitions for secure identity based encryption schemes and give several applications for such systems.

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.

Entity authentication and key distribution are central cryptographic problems in distributed computing -- but up until now, they have lacked even a meaningful definition. One consequence is that incorrect and inefficient protocols have proliferated. This paper provides the first treatment of these problems in the complexity-theoretic framework of modern cryptography. Addressed in detail are two problems of the symmetric, two-party setting: mutual authentication and authenticated key exchange. For each we present a definition, protocol, and proof that the protocol meets its goal, assuming the (minimal) assumption of pseudorandom function. When this assumption is appropriately instantiated, the protocols given are practical and efficient.

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 study notions and schemes for symmetric (ie. private key) encryption in a concrete security framework. We give four di erent notions of security against chosen plaintext attack and analyze the concrete complexity ofreductions among them, providing both upper and lower bounds, and obtaining tight relations. In this way we classify notions (even though polynomially reducible to each other) as stronger or weaker in terms of concrete security. Next we provide concrete security analyses of methods to encrypt using a block cipher, including the most popular encryption method, CBC. We establish tight bounds (meaning

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. We present a new protocol that allows two players to ex-change digital signatures over the Internet in a fair way, so that either each player gets the other’s signature, or neither player does. The ob-vious application is where the signatures represent items of value, for example, an electronic check or airline ticket. The protocol can also be adapted to exchange encrypted data. The protocol relies on a trusted third party, but is “optimistic, ” in that the third party is only needed in cases where one player attempts to cheat or simply crashes. A key feature of our protocol is that a player can always force a timely and fair termination, without the cooperation of the other player. 1

Given an arbitrary k-bit to k-bit trapdoor permutation f and a hash function, we exhibit an encryption scheme for which (i) any string x of length slightly less than k bits can be encrypted as f(rx), where rx is a simple probabilistic encoding of x depending on the hash function; and (ii) the scheme can be proven semantically secure assuming the hash function is \ideal. " Moreover, a slightly enhanced scheme is shown to have the property that the adversary can create ciphertexts only of strings for which she \knows " the corresponding plaintexts|such ascheme is not only semantically secure but also non-malleable and secure against chosen-ciphertext attack.

The Decision Diffie-Hellman assumption (ddh) is a gold mine. It enables one to construct efficient cryptographic systems with strong security properties. In this paper we survey the recent applications of DDH as well as known results regarding its security. We describe some open problems in this area. 1 Introduction An important goal of cryptography is to pin down the exact complexity assumptions used by cryptographic protocols. Consider the Diffie-Hellman key exchange protocol [12]: Alice and Bob fix a finite cyclic group G and a generator g. They respectively pick random a; b 2 [1; jGj] and exchange g a ; g b . The secret key is g ab . To totally break the protocol a passive eavesdropper, Eve, must compute the Diffie-Hellman function defined as: dh g (g a ; g b ) = g ab . We say that the group G satisfies the Computational Diffie-Hellman assumption (cdh) if no efficient algorithm can compute the function dh g (x; y) in G. Precise definitions are given in the next sectio...