Ate Pairing on Hyperelliptic Curves

Robert  Granger; Florian Hess; Roger Oyono; Nicolas Theriault; Fre Vercauteren

Ate Pairing on Hyperelliptic Curves

Robert Granger, Florian Hess, Roger Oyono, Nicolas Theriault, Fre Vercauteren

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

45 Citations (Scopus)

Abstract

In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller's algorithm can be up to $g$ times shorter than for the Tate pairing, with $g$ the genus of the curve, and the pairing is also automatically reduced, i.e., no final exponentiation is needed.

Translated title of the contribution	Ate Pairing on Hyperelliptic Curves
Original language	English
Title of host publication	Advances in Cryptology - EUROCRYPT 2007
Publisher	Springer Berlin Heidelberg
Pages	430-447
Volume	4515
Publication status	Published - 2007

Bibliographical note

Other page information: 430-447
Conference Proceedings/Title of Journal: Advances in Cryptology - EUROCRYPT 2007
Other identifier: 2000709

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@inproceedings{10fbf024b45d47d6800bfdc59f3fef52,

title = "Ate Pairing on Hyperelliptic Curves",

abstract = "In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller's algorithm can be up to $g$ times shorter than for the Tate pairing, with $g$ the genus of the curve, and the pairing is also automatically reduced, i.e., no final exponentiation is needed. ",

author = "Robert Granger and Florian Hess and Roger Oyono and Nicolas Theriault and Fre Vercauteren",

note = "Other page information: 430-447 Conference Proceedings/Title of Journal: Advances in Cryptology - EUROCRYPT 2007 Other identifier: 2000709",

year = "2007",

language = "English",

volume = "4515",

pages = "430--447",

booktitle = "Advances in Cryptology - EUROCRYPT 2007",

publisher = "Springer Berlin Heidelberg",

address = "Germany",

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TY - GEN

T1 - Ate Pairing on Hyperelliptic Curves

AU - Granger, Robert

AU - Hess, Florian

AU - Oyono, Roger

AU - Theriault, Nicolas

AU - Vercauteren, Fre

N1 - Other page information: 430-447 Conference Proceedings/Title of Journal: Advances in Cryptology - EUROCRYPT 2007 Other identifier: 2000709

PY - 2007

Y1 - 2007

N2 - In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller's algorithm can be up to $g$ times shorter than for the Tate pairing, with $g$ the genus of the curve, and the pairing is also automatically reduced, i.e., no final exponentiation is needed.

AB - In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller's algorithm can be up to $g$ times shorter than for the Tate pairing, with $g$ the genus of the curve, and the pairing is also automatically reduced, i.e., no final exponentiation is needed.

M3 - Conference Contribution (Conference Proceeding)

VL - 4515

SP - 430

EP - 447

BT - Advances in Cryptology - EUROCRYPT 2007

PB - Springer Berlin Heidelberg

ER -

Ate Pairing on Hyperelliptic Curves

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