Operations of Points on Elliptic Curve in Affine Coordinates

Pole DC	Wartość	Język
dc.contributor.author	Futa, Yuichi	-
dc.contributor.author	Okazaki, Hiroyuki	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2020-04-17T09:21:49Z	-
dc.date.available	2020-04-17T09:21:49Z	-
dc.date.issued	2019	-
dc.identifier.citation	Formalized Mathematics, Volume 27, Issue 3, Pages 315–320	pl
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/9017	-
dc.description.abstract	In this article, we formalize in Mizar [1], [2] a binary operation of points on an elliptic curve over GF(p) in affine coordinates. We show that the operation is unital, complementable and commutative. Elliptic curve cryptography [3], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security.	pl
dc.description.sponsorship	This work was supported by JSPS KAKENHI Grant Numbers JP15K00183 and JP17K00182.	pl
dc.language.iso	en	pl
dc.publisher	DeGruyter Open	pl
dc.rights	Uznanie autorstwa-Na tych samych warunkach 3.0 Polska	*
dc.rights.uri	http://creativecommons.org/licenses/by-sa/3.0/pl/	*
dc.subject	elliptic curve	pl
dc.subject	commutative operation	pl
dc.title	Operations of Points on Elliptic Curve in Affine Coordinates	pl
dc.type	Article	pl
dc.identifier.doi	10.2478/forma-2019-0026	-
dc.description.Affiliation	Yuichi Futa - Tokyo University of Technology, Tokyo, Japan	pl
dc.description.Affiliation	Hiroyuki Okazaki - Shinshu University, Nagano, Japan	pl
dc.description.Affiliation	Yasunari Shidama - Shinshu University, Nagano, Japan	pl
dc.description.references	Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8 17.	pl
dc.description.references	Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pak. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.	pl
dc.description.references	I. Blake, G. Seroussi, and N. Smart. Elliptic Curves in Cryptography. Number 265 in London Mathematical Society Lecture Note Series. Cambridge University Press, 1999.	pl
dc.description.references	Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Set of points on elliptic curve in projective coordinates. Formalized Mathematics, 19(3):131–138, 2011. doi:10.2478/v10037-011-0021-6.	pl
dc.description.references	Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, and Yasunari Shidama. Operations of points on elliptic curve in projective coordinates. Formalized Mathematics, 20(1): 87–95, 2012. doi:10.2478/v10037-012-0012-2.	pl
dc.description.references	Artur Korniłowicz. Recursive definitions. Part II. Formalized Mathematics, 12(2):167–172, 2004.	pl
dc.identifier.eissn	1898-9934	-
dc.description.volume	27	-
dc.description.issue	3	-
dc.description.firstpage	315	pl
dc.description.lastpage	320	pl
dc.identifier.citation2	Formalized Mathematics	pl
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