• Synonyms Tripartite key exchange Related Concepts
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    Pairing-Based Key Exchange
    Tanja Lange
    Coding Theory and Cryptology, Eindhoven Institute for
    the Protection of Systems and Information, Department
    of Mathematics and Computer Science, Technische
    Universiteit Eindhoven, Eindhoven, The Netherlands
    Synonyms
    Tripartite key exchange
    Related Concepts
    
    Diffie–Hellman Key Agreement
    ;
    
    Group Key Agree-
    ment
    ;
    
    Identity-Based Cryptosystems
    ;
    
    Identity-Based
    Encryption
    ;
    
    Pairings
    ;
    
    Secret
    Sharing
    Schemes
    ;
    
    Verifiable Secret Sharing
    ;
    
    Visual Secret Sharing Schemes
    Definition
    Pairing-based key exchange is a protocol based on public-
    key cryptography in which three or more participants
    establish a shared key via an insecure channel and cryp-
    tographic pairings are used. Tripartite key exchange is
    pairing-based key exchange for exactly three participants.
    Background
    In the s, the Weil and Tate
    
    pairings
    were seen as
    a means to attack cryptosystems based on certain elliptic
    curves. In particular the MOV attack [

    ] and the Frey–
    Rück attack [

    ] were used to break the
    
    elliptic curve
    discrete logarithm problem
    on supersingular curves or in
    general on curves with small embedding degree. Joux was
    the first to use pairings in a constructive manner when
    he proposed to use them in tripartite key exchange in
    [

    ]. Pairings have found widespread application (see the
    separate entry), in particular in
    
    identity-based cryptosys-
    tems
    and
    
    identity-based encryption
    .


    

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