The equivalence between the DHP and DLP for elliptic curves used in practical applications

NP Smart; F Vercauteren; A Muzereau

The equivalence between the DHP and DLP for elliptic curves used in practical applications

NP Smart
, F Vercauteren
, A Muzereau

Cryptography and Information Security

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

We re-examine the reduction of Maurer and Wolf of the Discrete Logarithm problem to the Diffie--Hellman problem. We give a precise estimate for the number of operations required in the reduction and use this to estimate the exact security of the elliptic curve variant of the Diffie--Hellman protocol for various elliptic curves defined in standards.

Translated title of the contribution	The equivalence between the DHP and DLP for elliptic curves used in practical applications
Original language	English
Pages (from-to)	50 - 72
Number of pages	22
Journal	LMS Journal of Computation and Mathematics
Volume	7
Publication status	Published - Mar 2004

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title = "The equivalence between the DHP and DLP for elliptic curves used in practical applications",

abstract = " We re-examine the reduction of Maurer and Wolf of the Discrete Logarithm problem to the Diffie--Hellman problem. We give a precise estimate for the number of operations required in the reduction and use this to estimate the exact security of the elliptic curve variant of the Diffie--Hellman protocol for various elliptic curves defined in standards. ",

author = "NP Smart and F Vercauteren and A Muzereau",

year = "2004",

month = mar,

language = "English",

volume = "7",

pages = "50 -- 72",

journal = "LMS Journal of Computation and Mathematics",

issn = "1461-1570",

publisher = "Cambridge University Press",

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TY - JOUR

T1 - The equivalence between the DHP and DLP for elliptic curves used in practical applications

AU - Smart, NP

AU - Vercauteren, F

AU - Muzereau, A

PY - 2004/3

Y1 - 2004/3

N2 - We re-examine the reduction of Maurer and Wolf of the Discrete Logarithm problem to the Diffie--Hellman problem. We give a precise estimate for the number of operations required in the reduction and use this to estimate the exact security of the elliptic curve variant of the Diffie--Hellman protocol for various elliptic curves defined in standards.

AB - We re-examine the reduction of Maurer and Wolf of the Discrete Logarithm problem to the Diffie--Hellman problem. We give a precise estimate for the number of operations required in the reduction and use this to estimate the exact security of the elliptic curve variant of the Diffie--Hellman protocol for various elliptic curves defined in standards.

M3 - Article (Academic Journal)

SN - 1461-1570

VL - 7

SP - 50

EP - 72

JO - LMS Journal of Computation and Mathematics

JF - LMS Journal of Computation and Mathematics

ER -

The equivalence between the DHP and DLP for elliptic curves used in practical applications

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