Abstract. We introduce a short signature scheme based on the Computational Diffie-Hellman assumption on certain elliptic and hyper-elliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signatures are typed in by a human or signatures are sent over a low-bandwidth channel. 1

In this paper we propose an identity(ID)-based signature scheme using gap Diffie-Hellman (GDH) groups. Our scheme is proved secure against existential forgery on adaptively chosen message and ID attack under the random oracle model.

We propose a simple algorithm to select group generators suitable for pairing-based cryptosystems. The selected parameters are shown to favor implementations of the Tate pairing that are at once conceptually simple and very efficient, with an observed performance about 2 to 10 times better than previously reported implementations.

Pairing-based cryptosystems depend on the existence of groups where the Decision Diffie-Hellman problem is easy to solve, but the Computational Diffie-Hellman problem is hard. Such is the case of elliptic curve groups whose embedding degree is large enough to maintain a good security level, but small enough for arithmetic operations to be feasible. However, the embedding degree is usually enormous, and the scarce previously known suitable elliptic groups had embedding degree k <= 6. In this note, we examine criteria for curves with larger k that generalize prior work by Miyaji et al. based on the properties of cyclotomic polynomials, and propose efficient representations for the underlying algebraic structures.

Abstract. Authenticated key exchange protocols tend to be either token based or password based. Token based schemes are often based on expensive (and irreplaceable) smart-card tokens, while password-only schemes require that a unique password is shared between every pair of correspondents. The magnetic strip swipe card and associated PIN number is a familiar and convenient format that motivates a combined “two-factor ” approach. Finally we suggest an extension of the scheme for use in a client-server scenario.

Joux's protocol [29] is a one round, tripartite key agreement protocol that is more bandwidth-efficient than any previous three-party key agreement protocol. But it is insecure, suffering from a simple man-in-the-middle attack. This paper shows how to make Joux's protocol secure, presenting several tripartite, authenticated key agreement protocols that still require only one round of communication and no signature computations. A pass-optimal authenticated and key confirmed tripartite protocol that generalises the station-to-station protocol is also presented. The security properties of the new protocols are studied using provable security methods and heuristic approaches. Applications for the protocols are also discussed.

Pairing-based cryptosystems rely on bilinear non-degenerate maps called pairings, such as the Tate and Weil pairings defined over certain elliptic curve groups. In this paper we show how to compress pairing values, how to couple this technique with that of point compression, and how to benefit from the compressed representation to speed up exponentiations involving pairing values, as required in many pairing based protocols.

The output of the Tate pairing on an elliptic curve over a nite eld is an element in the multiplicative group of an extension eld modulo a particular subgroup. One ordinarily powers this element to obtain a unique representative for the output coset, and performs any further necessary arithmetic in the extension eld. Rather than an obstruction, we show to the contrary that one can exploit this quotient group to eliminate the nal powering, to speed up exponentiations and to obtain a simple compression of pairing values which is useful during interactive identity-based cryptographic protocols. Speci cally we demonstrate that methods available for fast point multiplication on elliptic curves such as mixed addition, signed digit representations and Frobenius expansions, all transfer easily to the quotient group, and provide a signi cant improvement over the arithmetic of the extension eld.

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Recently, Shim proposed a tripartite authenticated key agreement protocol from Weil pairing to overcome the security flaw in Joux's protocol. Later, Shim also proposed...