A note on Schoenmakers algorithm for multi exponentiation

Srinivasa Rao Subramanya Rao

doi:10.5220/0005566903840391

A note on Schoenmakers algorithm for multi exponentiation

Srinivasa Rao Subramanya Rao^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Citations (Scopus)

Abstract

In this paper, we provide a triple scalar multiplication analogue of the simultaneous double scalar Schoenmakers' algorithm for multiexponentiation. We analyse this algorithm to show that on the average, the triple scalar Schoenmakers' algorithm is more expensive than the straight forward method of computing the individual exponents and then computing the requisite product, thus making it undesirable for use in resource constrained environments. We also show the derivation of the Schoenmakers' algorithm for simultaneous double scalar multiplication and this is then used to construct the triple scalar multiplication analogue.

Original language	English
Title of host publication	SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015
Editors	Mohammad S. Obaidat, Pascal Lorenz, Pierangela Samarati
Publisher	SciTePress
Pages	384-391
Number of pages	8
ISBN (Electronic)	9789897581175
DOIs	https://doi.org/10.5220/0005566903840391
Publication status	Published - 2015
Event	12th International Conference on Security and Cryptography, SECRYPT 2015 - Colmar, Alsace, France Duration: 20 Jul 2015 → 22 Jul 2015

Publication series

Name	SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015

Conference

Conference	12th International Conference on Security and Cryptography, SECRYPT 2015
Country/Territory	France
City	Colmar, Alsace
Period	20/07/15 → 22/07/15

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10.5220/0005566903840391

Cite this

Rao, S. R. S. (2015). A note on Schoenmakers algorithm for multi exponentiation. In M. S. Obaidat, P. Lorenz, & P. Samarati (Eds.), SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015 (pp. 384-391). (SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015). SciTePress. https://doi.org/10.5220/0005566903840391

Rao, Srinivasa Rao Subramanya. / A note on Schoenmakers algorithm for multi exponentiation. SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015. editor / Mohammad S. Obaidat ; Pascal Lorenz ; Pierangela Samarati. SciTePress, 2015. pp. 384-391 (SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015).

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title = "A note on Schoenmakers algorithm for multi exponentiation",

abstract = "In this paper, we provide a triple scalar multiplication analogue of the simultaneous double scalar Schoenmakers' algorithm for multiexponentiation. We analyse this algorithm to show that on the average, the triple scalar Schoenmakers' algorithm is more expensive than the straight forward method of computing the individual exponents and then computing the requisite product, thus making it undesirable for use in resource constrained environments. We also show the derivation of the Schoenmakers' algorithm for simultaneous double scalar multiplication and this is then used to construct the triple scalar multiplication analogue.",

keywords = "Double scalar multiplication, Elliptic curve cryptography, Montgomery curves, Multiexponentiation, Schoenmakers' algorithm, Smart cards, Triple scalar multiplication",

author = "Rao, {Srinivasa Rao Subramanya}",

note = "Publisher Copyright: {\textcopyright} Copyright 2015 SCITEPRESS - Science and Technology Publications. All rights reserved.; 12th International Conference on Security and Cryptography, SECRYPT 2015 ; Conference date: 20-07-2015 Through 22-07-2015",

year = "2015",

doi = "10.5220/0005566903840391",

language = "English",

series = "SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015",

publisher = "SciTePress",

pages = "384--391",

editor = "Obaidat, {Mohammad S.} and Pascal Lorenz and Pierangela Samarati",

booktitle = "SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015",

}

Rao, SRS 2015, A note on Schoenmakers algorithm for multi exponentiation. in MS Obaidat, P Lorenz & P Samarati (eds), SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015. SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015, SciTePress, pp. 384-391, 12th International Conference on Security and Cryptography, SECRYPT 2015, Colmar, Alsace, France, 20/07/15. https://doi.org/10.5220/0005566903840391

A note on Schoenmakers algorithm for multi exponentiation. / Rao, Srinivasa Rao Subramanya.
SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015. ed. / Mohammad S. Obaidat; Pascal Lorenz; Pierangela Samarati. SciTePress, 2015. p. 384-391 (SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - A note on Schoenmakers algorithm for multi exponentiation

AU - Rao, Srinivasa Rao Subramanya

PY - 2015

Y1 - 2015

N2 - In this paper, we provide a triple scalar multiplication analogue of the simultaneous double scalar Schoenmakers' algorithm for multiexponentiation. We analyse this algorithm to show that on the average, the triple scalar Schoenmakers' algorithm is more expensive than the straight forward method of computing the individual exponents and then computing the requisite product, thus making it undesirable for use in resource constrained environments. We also show the derivation of the Schoenmakers' algorithm for simultaneous double scalar multiplication and this is then used to construct the triple scalar multiplication analogue.

AB - In this paper, we provide a triple scalar multiplication analogue of the simultaneous double scalar Schoenmakers' algorithm for multiexponentiation. We analyse this algorithm to show that on the average, the triple scalar Schoenmakers' algorithm is more expensive than the straight forward method of computing the individual exponents and then computing the requisite product, thus making it undesirable for use in resource constrained environments. We also show the derivation of the Schoenmakers' algorithm for simultaneous double scalar multiplication and this is then used to construct the triple scalar multiplication analogue.

KW - Double scalar multiplication

KW - Elliptic curve cryptography

KW - Montgomery curves

KW - Multiexponentiation

KW - Schoenmakers' algorithm

KW - Smart cards

KW - Triple scalar multiplication

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U2 - 10.5220/0005566903840391

DO - 10.5220/0005566903840391

M3 - Conference contribution

T3 - SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015

SP - 384

EP - 391

BT - SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015

A2 - Obaidat, Mohammad S.

A2 - Lorenz, Pascal

A2 - Samarati, Pierangela

PB - SciTePress

T2 - 12th International Conference on Security and Cryptography, SECRYPT 2015

Y2 - 20 July 2015 through 22 July 2015

ER -

Rao SRS. A note on Schoenmakers algorithm for multi exponentiation. In Obaidat MS, Lorenz P, Samarati P, editors, SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015. SciTePress. 2015. p. 384-391. (SECRYPT 2015 - 12th International Conference on Security and Cryptography, Proceedings; Part of 12th International Joint Conference on e-Business and Telecommunications, ICETE 2015). doi: 10.5220/0005566903840391

A note on Schoenmakers algorithm for multi exponentiation

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