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.

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.

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...

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

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

A group signature scheme allows a group member to sign messages anonymously on behalf of the group. However, in the case of a dispute, the identity of a signature’s originator can be revealed (only) by a designated entity. The interactive counterparts of group signatures are identity escrow schemes or group identification scheme with revocable anonymity. This work introduces a new provably secure group signature and a companion identity escrow scheme that are significantly more efficient than the state of the art. In its interactive, identity escrow form, our scheme is proven secure and coalition-resistant under the strong RSA and the decisional Diffie-Hellman assumptions. The security of the noninteractive variant, i.e., the group signature scheme, relies additionally on the Fiat-Shamir heuristic (also known as the random oracle model).

Abstract not found

Abstract. We construct a short group signature scheme. Signatures in our scheme are approximately the size of a standard RSA signature with the same security. Security of our group signature is based on the Strong Diffie-Hellman assumption and a new assumption in bilinear groups called the Decision Linear assumption. We prove security of our system, in the random oracle model, using a variant of the security definition for group signatures recently given by Bellare, Micciancio, and Warinschi. 1

. Incorporating the property of untraceability of payments into off-line electronic cash systems has turned out to be no easy matter. Two key concepts have been proposed in order to attain the same level of security against double-spending as can be trivially attained in systems with full traceability of payments. The first of these, one-show blind signatures, ensures traceability of double-spenders after the fact. The realizations of this concept that have been proposed unfortunately require either a great sacrifice in efficiency or seem to have questionable security, if not both. The second concept, wallets with observers, guarantees prior restraint of double-spending, while still offering traceability of double-spenders after the fact in case tamper-resistance is compromised. No realization of this concept has yet been proposed in literature, which is a serious problem. It seems that the known cash systems cannot be extended to this important setting without significantly worsening ...

In this paper, we address the question of providing security proofs for signature schemes in the so-called random oracle model [1]. In particular, we establish the generality of this technique against adaptively chosen message attacks. Our main application achieves such a security proof for a slight variant of the El Gamal signature scheme [3] where committed values are hashed together with the message. This is a rather surprising result since the original El Gamal is, as RSA [11], subject to existential forgery.