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23
Short signatures from the Weil pairing
, 2001
"... Abstract. We introduce a short signature scheme based on the Computational DiffieHellman assumption on certain elliptic and hyperelliptic 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 signa ..."
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Cited by 597 (29 self)
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Abstract. We introduce a short signature scheme based on the Computational DiffieHellman assumption on certain elliptic and hyperelliptic 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 lowbandwidth channel. 1
An IdentityBased Signature from Gap DiffieHellman Groups
 Public Key Cryptography  PKC 2003, LNCS 2139
, 2002
"... In this paper we propose an identity(ID)based signature scheme using gap DiffieHellman (GDH) groups. Our scheme is proved secure against existential forgery on adaptively chosen message and ID attack under the random oracle model. ..."
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Cited by 154 (4 self)
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In this paper we propose an identity(ID)based signature scheme using gap DiffieHellman (GDH) groups. Our scheme is proved secure against existential forgery on adaptively chosen message and ID attack under the random oracle model.
Constructing Elliptic Curves with Prescribed Embedding Degrees
, 2002
"... Pairingbased cryptosystems depend on the existence of groups where the Decision DiffieHellman problem is easy to solve, but the Computational DiffieHellman problem is hard. Such is the case of elliptic curve groups whose embedding degree is large enough to maintain a good security level, but smal ..."
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Cited by 55 (17 self)
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Pairingbased cryptosystems depend on the existence of groups where the Decision DiffieHellman problem is easy to solve, but the Computational DiffieHellman 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.
Authenticated IDbased Key Exchange and remote login with insecure token and PIN number, Cryptology ePrint Archive
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On the Selection of PairingFriendly Groups
, 2003
"... We propose a simple algorithm to select group generators suitable for pairingbased 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 prev ..."
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Cited by 48 (13 self)
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We propose a simple algorithm to select group generators suitable for pairingbased 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.
Compressed Pairings
 In Advances in cryptology – Crypto’2004
, 2004
"... Pairingbased cryptosystems rely on bilinear nondegenerate 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 f ..."
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Cited by 42 (8 self)
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Pairingbased cryptosystems rely on bilinear nondegenerate 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.
Tripartite Authenticated Key Agreement Protocols from Pairings
, 2002
"... Joux's protocol [29] is a one round, tripartite key agreement protocol that is more bandwidthefficient than any previous threeparty key agreement protocol. But it is insecure, suffering from a simple maninthemiddle attack. This paper shows how to make Joux's protocol secure, presenti ..."
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Cited by 38 (1 self)
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Joux's protocol [29] is a one round, tripartite key agreement protocol that is more bandwidthefficient than any previous threeparty key agreement protocol. But it is insecure, suffering from a simple maninthemiddle 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 passoptimal authenticated and key confirmed tripartite protocol that generalises the stationtostation 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.
On Small Characteristic Algebraic Tori in PairingBased Cryptography
, 2004
"... 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 arithmet ..."
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Cited by 32 (3 self)
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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 identitybased 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.
Security Analysis of Shim's Authenticated Key Agreement Protocols from Pairings
, 2003
"... 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... ..."
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Cited by 26 (0 self)
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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...