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The Decision Diffie-Hellman Problem (1998)

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by Dan Boneh
Citations:237 - 7 self
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BibTeX

@INPROCEEDINGS{Boneh98thedecision,
    author = {Dan Boneh},
    title = {The Decision Diffie-Hellman Problem},
    booktitle = {},
    year = {1998},
    pages = {48--63},
    publisher = {Springer-Verlag}
}

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Abstract

The Decision Diffie-Hellman assumption (ddh) is a gold mine. It enables one to construct efficient cryptographic systems with strong security properties. In this paper we survey the recent applications of DDH as well as known results regarding its security. We describe some open problems in this area. 1 Introduction An important goal of cryptography is to pin down the exact complexity assumptions used by cryptographic protocols. Consider the Diffie-Hellman key exchange protocol [12]: Alice and Bob fix a finite cyclic group G and a generator g. They respectively pick random a; b 2 [1; jGj] and exchange g a ; g b . The secret key is g ab . To totally break the protocol a passive eavesdropper, Eve, must compute the Diffie-Hellman function defined as: dh g (g a ; g b ) = g ab . We say that the group G satisfies the Computational Diffie-Hellman assumption (cdh) if no efficient algorithm can compute the function dh g (x; y) in G. Precise definitions are given in the next sectio...

Keyphrases

decision diffie-hellman problem    recent application    diffie-hellman key exchange protocol    efficient cryptographic system    function dh    open problem    secret key    strong security property    exact complexity assumption    passive eavesdropper    finite cyclic group    cryptographic protocol    precise definition    computational diffie-hellman assumption    important goal    gold mine    decision diffie-hellman assumption    efficient algorithm    diffie-hellman function    next sectio   

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