## An Identity Based Authenticated Key Agreement Protocol Based on the Weil Pairing (2001)

Venue: | Electronics Letters |

Citations: | 66 - 2 self |

### BibTeX

@ARTICLE{Smart01anidentity,

author = {N. P. Smart},

title = {An Identity Based Authenticated Key Agreement Protocol Based on the Weil Pairing},

journal = {Electronics Letters},

year = {2001},

volume = {38},

pages = {630--632}

}

### Years of Citing Articles

### OpenURL

### Abstract

We describe an ID based authenticated two pass key agreement protocol which makes use of the Weil pairing. The protocol is described and its properties are discussed including the ability to add key confirmation.

### Citations

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Citation Context ...nt is one of the fundamental cryptographic primitives after encryption and digital signatures. The first modern protocol for key agreement was the Diffie-Hellman protocol given in their seminal paper =-=[4]-=-, however this protocol needs to be used with care. Over the years a number of security properties have been seen to be important in key agreement protocols. For example the basic Diffie-Hellman proto... |

1227 | Identity-Based Encryption from the Weil Pairing
- Boneh, Franklin
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(Show Context)
Citation Context ...lem of authenticating the static public keys. But this latter problem can be solved using a traditional approach based on a public key infrastructure (PKI). Recently, Cocks [3] and Boneh and Franklin =-=[1]-=- have proposed two identity based encryption schemes which potentially allow the replacement of a PKI with a system Key words and phrases. cryptography, ID-based cryptography, key agreement, elliptic ... |

593 | Short signatures from the Weil pairing
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Citation Context ... protocol based on the Weil pairing on supersingular curves. Since Joux's paper a number of other applications have arisen, including an identity based encryption scheme [1] and a signature algorithm =-=[2]-=-. The extension to higher genus curves has also recently been fully explored in [5]. 3. The AK and AKC Protocols Suppose we have a subgroup G of an elliptic curve for which the modified Weil pairingse... |

311 |
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Citation Context ...r the key generation centre to decrypt messages at will. 2. The Weil Pairing In this section we shall summarize the properties we require of the Weil pairing, much of the details can be found in [1], =-=[8]-=- and [10]. We let G denote a prime order subgroup of an elliptic curve E over the field F q . Let the order of G be denoted by l and define k to be the smallest integer such that ljq k \Gamma 1: In pr... |

280 |
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(Show Context)
Citation Context ...wo pass identity based authenticated key agreement protocol. Our protocol is based on the Weil pairing and combines the ideas of Boneh and Franklin with the tripartite Diffie-Hellman protocol of Joux =-=[6]-=-. The message flows in our new protocol are identical with the message flows of the two pass elliptic curve based unauthenticated Diffie-Hellman protocol, hence from the outside it looks like a Diffie... |

269 |
New directions in cryptography
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(Show Context)
Citation Context ...eement is one of the fundamental cryptographic primitives after encryption and digital signatures. The rst modern protocol for key agreement was the Di e-Hellman protocol given in their seminal paper =-=[4]-=-, however this protocol needs to be used with care. Over the years a number of security properties have been seen to be important inkey agreement protocols. For example the basic Di e-Hellman protocol... |

219 | An identity based encryption scheme based on quadratic residues
- Cocks
- 2001
(Show Context)
Citation Context ...key is replaced by the problem of authenticating the static public keys. But this latter problem can be solved using a traditional approach based on a public key infrastructure (PKI). Recently, Cocks =-=[3]-=- and Boneh and Franklin [1] have proposed two identity based encryption schemes which potentially allow the replacement of a PKI with a system Key words and phrases. cryptography, ID-based cryptograph... |

122 | An Efficient Protocol for Authenticated Key Agreement”, Designs, Codes and Cryptography volume 28
- Law, Menezes, et al.
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(Show Context)
Citation Context ...municating parties. A simple solution would be to combine a key agreement protocol with a digital signature scheme to obtain an authenticated key agreement protocol (or AK protocol in the language of =-=[7]-=-). This solution has a number of problems, not least of which is the fact that the message lengths are now much greater than in the standard Diffie-Hellman protocol. In [7] Law, Menezes, Qu, Solinas a... |

90 | Supersingular curves in cryptography
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(Show Context)
Citation Context ...umber of other applications have arisen, including an identity based encryption scheme [1] and a signature algorithm [2]. The extension to higher genus curves has also recently been fully explored in =-=[5]-=-. 3. The AK and AKC Protocols Suppose we have a subgroup G of an elliptic curve for which the modified Weil pairingse maps into the finite field F q k . We assume that q k is large enough to make solv... |

76 |
The arithmetic of elliptic curves, GTM 106
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(Show Context)
Citation Context ...y generation centre to decrypt messages at will. 2. The Weil Pairing In this section we shall summarize the properties we require of the Weil pairing, much of the details can be found in [1], [8] and =-=[10]-=-. We let G denote a prime order subgroup of an elliptic curve E over the field F q . Let the order of G be denoted by l and define k to be the smallest integer such that ljq k \Gamma 1: In practical i... |

66 |
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Citation Context ...ard Weil pairing e(P; Q), but it does hold for the modified Weil pairingse(P; Q). That the Weil pairing is efficiently computable follows from an unpublished, but much referenced, algorithm of Miller =-=[9]-=-. The modified Weil pairing that we use is defined in [1] and it is computed in exactly the same way by using Miller's algorithm. Originally the existence of the Weil pairing was thought to be a bad t... |

42 |
A one round protocol for tripartite Die-Hellman
- Joux
- 2000
(Show Context)
Citation Context ...a two passidentity based authenticated key agreement protocol. Our protocol is based on the Weil pairing and combines the ideas of Boneh and Franklin with the tripartite Di e-Hellman protocol of Joux =-=[6]-=-. The message ows in our new protocol are identical with the message ows of the two pass elliptic curve based unauthenticated Di e-Hellman protocol, hence from the outside it looks like a Di e-Hellman... |

3 |
An ef cient protocol for authenticated key agreement
- Law, Menezes, et al.
- 1998
(Show Context)
Citation Context ...municating parties. A simple solution would be to combine a key agreement protocol with a digital signature scheme to obtain an authenticated key agreement protocol (or AK protocol in the language of =-=[7]-=-). This solution has anumber of problems, not least of which is the fact that the message lengths are now much greater than in the standard Di e-Hellman protocol. In [7] Law, Menezes, Qu, Solinas and ... |