On Montgomery-like representations for elliptic curves over GF(2k)

M Stam

On Montgomery-like representations for elliptic curves over GF(2^k)

M Stam

Department of Computer Science

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

24 Citations (Scopus)

Abstract

This paper discusses representations for computation on non-supersingular elliptic curves over binary fields, where computations are performed on the $x$-coordinates only. We discuss existing methods and present a new one, giving rise to a faster addition routine than previous Montgomery-representations. As a result a double exponentiation routine is described that requires 8.5 field multiplications per exponent bit, but that does not allow easy $y$-coordinate recovery. For comparison, we also give a brief update of the survey by Hankerson et al. and conclude that, for non-constrained devices, using a Montgomery-representation is slower for both single and double exponentiation than projective methods with $y$-coordinate.

Translated title of the contribution	On {M}ontgomery-like representations for elliptic curves over {$GF(2^k)$}
Original language	English
Title of host publication	Public Key Cryptography - PKC 2003
Publisher	Springer Berlin Heidelberg
Pages	240 - 253
Number of pages	13
Volume	2567
ISBN (Print)	354000324X
Publication status	Published - Jan 2003

Bibliographical note

Conference Proceedings/Title of Journal: Public Key Cryptography - PKC 2003, 6th International Workshop
on Theory and Practice in Public Key Cryptography, Miami, FL,
USA, January 6-8, 2003, Proceedings

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Cite this

@inproceedings{35d87e91d23a4a9e868d1f30d96363b8,

title = "On Montgomery-like representations for elliptic curves over GF(2k)",

abstract = " This paper discusses representations for computation on non-supersingular elliptic curves over binary fields, where computations are performed on the $x$-coordinates only. We discuss existing methods and present a new one, giving rise to a faster addition routine than previous Montgomery-representations. As a result a double exponentiation routine is described that requires 8.5 field multiplications per exponent bit, but that does not allow easy $y$-coordinate recovery. For comparison, we also give a brief update of the survey by Hankerson et al. and conclude that, for non-constrained devices, using a Montgomery-representation is slower for both single and double exponentiation than projective methods with $y$-coordinate. ",

author = "M Stam",

note = "Conference Proceedings/Title of Journal: Public Key Cryptography - PKC 2003, 6th International Workshop on Theory and Practice in Public Key Cryptography, Miami, FL, USA, January 6-8, 2003, Proceedings",

year = "2003",

month = jan,

language = "English",

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volume = "2567",

pages = "240 -- 253",

booktitle = "Public Key Cryptography - PKC 2003",

publisher = "Springer Berlin Heidelberg",

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TY - GEN

T1 - On Montgomery-like representations for elliptic curves over GF(2k)

AU - Stam, M

N1 - Conference Proceedings/Title of Journal: Public Key Cryptography - PKC 2003, 6th International Workshop on Theory and Practice in Public Key Cryptography, Miami, FL, USA, January 6-8, 2003, Proceedings

PY - 2003/1

Y1 - 2003/1

N2 - This paper discusses representations for computation on non-supersingular elliptic curves over binary fields, where computations are performed on the $x$-coordinates only. We discuss existing methods and present a new one, giving rise to a faster addition routine than previous Montgomery-representations. As a result a double exponentiation routine is described that requires 8.5 field multiplications per exponent bit, but that does not allow easy $y$-coordinate recovery. For comparison, we also give a brief update of the survey by Hankerson et al. and conclude that, for non-constrained devices, using a Montgomery-representation is slower for both single and double exponentiation than projective methods with $y$-coordinate.

AB - This paper discusses representations for computation on non-supersingular elliptic curves over binary fields, where computations are performed on the $x$-coordinates only. We discuss existing methods and present a new one, giving rise to a faster addition routine than previous Montgomery-representations. As a result a double exponentiation routine is described that requires 8.5 field multiplications per exponent bit, but that does not allow easy $y$-coordinate recovery. For comparison, we also give a brief update of the survey by Hankerson et al. and conclude that, for non-constrained devices, using a Montgomery-representation is slower for both single and double exponentiation than projective methods with $y$-coordinate.

M3 - Conference Contribution (Conference Proceeding)

SN - 354000324X

VL - 2567

SP - 240

EP - 253

BT - Public Key Cryptography - PKC 2003

PB - Springer Berlin Heidelberg

ER -