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Inverted Edwards Coordinates (Maire Form of an Elliptic Curve).pdf (357.28 KB)
ETD Abstract Container
Abstract Header
Inverted Edwards Coordinates (Maire Model of an Elliptic Curve)
Author Info
Maire, Steven M
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=case1396888557
Abstract Details
Year and Degree
2014, Master of Sciences, Case Western Reserve University, Applied Mathematics.
Abstract
Edwards curves are a fairly new way of expressing a family of elliptic curves that contain extremely desirable cryptographic properties over other forms that have been used. The most notable is the notion of a complete and unified addition law. This property makes Edwards curves extremely strong against side-channel attacks. In the analysis and continual development of Edwards curves, it has been seen in the original Edwards form that the use of inverted coordinates creates a more efficient addition/doubling algorithm. Using inverted coordinates, the field oper- ations drop from 10M + 1S (given correctly chosen curve parameters), to 9M + 1S. The sarcrifice is the loss of completeness, but unification remains. This pa- per examines the use of the inverted coordinates system over the binary Edwards form, and shows the underlying advantages of this transformation
Committee
David Singer, PhD (Advisor)
Elisabeth Werner, PhD (Committee Member)
Johnathan Duncan, PhD (Committee Member)
Pages
30 p.
Subject Headings
Computer Science
;
Mathematics
Keywords
elliptic curves
;
elliptic curve cryptography
;
edwards curves
;
ECDHKE
;
ECDSA
;
maire form
;
elliptic addition
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Citations
Maire, S. M. (2014).
Inverted Edwards Coordinates (Maire Model of an Elliptic Curve)
[Master's thesis, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1396888557
APA Style (7th edition)
Maire, Steven.
Inverted Edwards Coordinates (Maire Model of an Elliptic Curve).
2014. Case Western Reserve University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=case1396888557.
MLA Style (8th edition)
Maire, Steven. "Inverted Edwards Coordinates (Maire Model of an Elliptic Curve)." Master's thesis, Case Western Reserve University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=case1396888557
Chicago Manual of Style (17th edition)
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Document number:
case1396888557
Download Count:
920
Copyright Info
© 2014, some rights reserved.
Inverted Edwards Coordinates (Maire Model of an Elliptic Curve) by Steven M Maire is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.