Showing papers on "Weil pairing published in 2004"

Short Signatures from the Weil Pairing

Abstract: We introduce a short signature scheme based on the Computational Diffie–Hellman assumption on certain elliptic and hyperelliptic curves. For standard security parameters, the signature length is about half that of a DSA signature with a similar level of security. Our short signature scheme is designed for systems where signatures are typed in by a human or are sent over a low-bandwidth channel. We survey a number of properties of our signature scheme such as signature aggregation and batch verification.

The Weil Pairing, and Its Efficient Calculation

Abstract: The Weil Pairing, first introduced by Andre Weil in 1940, plays an important role in the theoretical study of the arithmetic of elliptic curves and Abelian varieties. It has also recently become extremely useful in cryptologic constructions related to those objects. This paper gives the definition of the Weil Pairing, describes efficient algorithms to calculate it, gives two applications, and describes the motivation to considering it.

Pairing-Based Cryptographic Protocols : A Survey.

Abstract: The bilinear pairing such as Weil pairing or Tate pairing on elliptic and hyperelliptic curves have recently been found applications in design of cryptographic protocols. In this survey, we have tried to cover different cryptographic protocols based on bilinear pairings which possess, to the best of our knowledge, proper security proofs in the existing security models.

A ring signature scheme using bilinear pairings

Abstract: The bilinear pairings such as Weil pairing or Tate pairing over elliptic curves and hyperelliptic curves have been found various applications in cryptography very recently. Ring signature is a very useful tool to provide the user's anonymity and the signer's privacy. In this paper, we propose a ring signature scheme based on the bilinear pairings, which is secure against chosen message attacks without random oracles. Moreover, we use this ring signature scheme to construct a concurrent signature scheme for fair exchange of signatures.

Weil pairing for Drinfeld modules

Abstract: As is well-known, there exists a Weil pairing for elliptic curves which is a perfect bilinear form from the m-torsion of the elliptic curve E to the m-th roots of unity. In this paper we will show how Anderson’s paper [1] gives rise to an analogue of this pairing for Drinfeld modules.

Efficient and Forward-Secure Identity-Based Signcryption.

Abstract: Several signcryption schemes proposed in the literature are known to lack semantic security, and semantically secure signcryption schemes tend to be more computationally expensive. In fact, devising an efficient signcryption scheme providing both public verifiability and forward security was until now an open problem. In this paper, we show how a particular kind of signcryption scheme may become completely insecure when implemented with certain efficient instantiations of the Tate or Weil pairing. We also address the drawbacks of the secure schemes by proposing efficient, semantically and forward-secure signcryption schemes, in both transferable and non-transferable form, that can be realised on top of any pairing instantiation. As a bonus, we also derive from them a new, efficient identity-based signature scheme.

Improved Weil and Tate pairings for elliptic and hyperelliptic curves

Abstract: We present algorithms for computing the squared Weil and Tate pairings on elliptic curves and the squared Tate pairing on hyperelliptic curves. The squared pairings introduced in this paper have the advantage that our algorithms for evaluating them are deterministic and do not depend on a random choice of points. Our algorithm to evaluate the squared Weil pairing is about 20% more efficient than the standard Weil pairing. Our algorithm for the squared Tate pairing on elliptic curves matches the efficiency of the algorithm given by Barreto, Lynn, and Scott in the case of arbitrary base points where their denominator cancellation technique does not apply. Our algorithm for the squared Tate pairing for hyperelliptic curves is the first detailed implementation of the pairing for general hyperelliptic curves of genus 2, and saves an estimated 30% over the standard algorithm.

Secure Bilinear Diffie-Hellman Bits

Abstract: The Weil and Tate pairings are a popular new gadget in cryptography and have found many applications, including identity-based cryptography. In particular, the pairings have been used for key exchange protocols.

Threshold Password-Based Authentication Using Bilinear Pairings

Abstract: We present a new threshold password-based authentication protocol that allows a roaming user(a user who accesses a network from different client terminals) to download a private key from remote servers with knowledge of only his identity and password. He does not need to carry the smart card storing his private information. We aim that a protocol has to allow a user to get his private key from the servers, even if some of the servers are compromised under the multi-server roaming system. In this paper, we firstly suggest a threshold password-only roaming protocol using (k,n)-threshold scheme which only k honest servers or more are engaged to reconstruct a secret key. Our scheme is based on bilinear pairings which could be built from Weil pairing or Tate pairing.

An Improved Identification Scheme

Abstract: Kim and Kim recently proposed a new identification scheme based on the Gap Diffie-Hellman problem, and proved that their scheme is secure against active attacks if the Gap Diffie-Hellman problem is intractable. However, their identification scheme is NOT secure in fact. In this paper, we first point out the reason why their scheme is not secure, and then improve their scheme such that the modified scheme is secure against active attacks if the Gap Diffie-Hellman problem is intractable.

Drinfeld modular curve and Weil pairing

Abstract: In this paper we describe the compactification of the Drinfeld modular curve. This compactification is analogous to the compactification of the classical modular curve given by Katz and Mazur. We show how the Weil pairing on Drinfeld modules that we defined in earlier work gives rise to a map on the Drinfeld modular curve. We introduce the Tate-Drinfeld module and show how this describes the formal neighbourhood of the scheme of cusps of the Drinfeld modular curve.

A new threshold proxy signature scheme from bilinear pairings

Abstract: Based on the GDH signature (short signature scheme) a probabilistic signature scheme is proposed in this paper with security proof. Then a new threshold proxy signature from bilinear pairings is proposed as well by using the new probabilistic signature scheme and the properties of the Gap Diffie-Hellman (GDH) group (where the Computational Diffie-Hellman problem is hard but the Decisional Diffie-Hellman problem is easy to solve). Our constructions are based on the recently proposed GDH signature scheme of Bonel et al.’s article. Bilinear pairings could be built from Weil pairing or Tate pairing. So most our constructions would be simpler, but still with high security. The proposed threshold proxy signature is the first one which is built from bilinear pairings. At the end of this paper security and performance of the threshold proxy signature scheme is also analyzed.

Escrow-Free Encryption Supporting Cryptographic Workflow.

Abstract: Since Boneh and Franklin published their seminal paper on identity based encryption (IBE) using the Weil pairing, there has been a great deal of interest in cryptographic primitives based on elliptic-curve pairings. One particularly interesting application has been to control access to data, via possibly complex policies. In this paper we continue the research in this vein. We present an encryption scheme such that the receiver of an encrypted message can only decrypt if it satisfies a particular policy chosen by the sender at the time of encryption. Unlike standard IBE, our encryption scheme is escrow free in that no credential-issuing authority (or colluding set of credential-issuing authorities) is able to decrypt ciphertexts itself, providing the users' public keys are properly certified. In addition we describe a security model for the scenario in question and provide proofs of security for our scheme (in the random oracle model).

A new threshold proxy signature scheme from bilinear pairings

Abstract: Based on the GDH signature (short signature scheme) a probabilistic signature scheme is proposed in this paper with security proof. Then a new threshold proxy signature from bilinear pairings is proposed as well by using the new probabilistic signature scheme and the properties of the Gap Diffie-Hellman (GDH) group (where the Computational Diffie-Hellman problem is hard but the Decisional Diffie-Hellman problem is easy to solve). Our constructions are based on the recently proposed GDH signature scheme of Bonel et al.'s article. Bilinear pairings could be built from Weil pairing or Tate pairing. So most our constructions would be simpler, but still with high security. The proposed threshold proxy signature is the first one which is built from bilinear pairings. At the end of this paper security and performance of the threshold proxy signature scheme is also analyzed.