{"id":163635,"date":"2012-06-01T00:00:00","date_gmt":"2012-06-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/implementing-4-dimensional-glv-method-on-gls-elliptic-curves-with-j-invariant-0\/"},"modified":"2018-10-16T20:04:11","modified_gmt":"2018-10-17T03:04:11","slug":"implementing-4-dimensional-glv-method-on-gls-elliptic-curves-with-j-invariant-0","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/implementing-4-dimensional-glv-method-on-gls-elliptic-curves-with-j-invariant-0\/","title":{"rendered":"Implementing 4-Dimensional GLV Method on GLS Elliptic Curves with j-Invariant 0"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The Gallant-Lambert-Vanstone (GLV) method is a very efficient technique for accelerating point multiplication on elliptic curves with efficiently computable endomorphisms. Galbraith, Lin and Scott (J. Cryptol. 24(3), 446-469 (2011)) showed that point multiplication exploiting the 2-dimensional GLV method on a large class of curves over GF(p<sup>2<\/sup>) was faster than the standard method on general elliptic curves over GF(p), and left as an open problem to study the case of 4-dimensional GLV on special curves (e.g., j(E) = 0) over GF(p<sup>2<\/sup>). We study the above problem in this paper. We show how to get the 4-dimensional GLV decomposition with proper decomposed coefficients, and thus reduce the number of doublings for point multiplication on these curves to only a quarter. The resulting implementation shows that the 4-dimensional GLV method on a GLS curve runs in about 0.78 the time of the 2-dimensional GLV method on the same curve and in between 0.78-0.87 the time of the 2-dimensional GLV method using the standard method over GF(p). In particular, our implementation reduces by up to 27% the time of the previously fastest implementation of point multiplication on x86-64 processors due to Longa and Gebotys (CHES2010).<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Gallant-Lambert-Vanstone (GLV) method is a very efficient technique for accelerating point multiplication on elliptic curves with efficiently computable endomorphisms. Galbraith, Lin and Scott (J. Cryptol. 24(3), 446-469 (2011)) showed that point multiplication exploiting the 2-dimensional GLV method on a large class of curves over GF(p2) was faster than the standard method on general elliptic [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13558],"msr-publication-type":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-163635","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-security-privacy-cryptography","msr-locale-en_us"],"msr_publishername":"Springer","msr_edition":"Journal of Designs, Codes and 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Hu","user_id":0,"rest_url":false},{"type":"user_nicename","value":"plonga","user_id":33271,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=plonga"},{"type":"text","value":"Maozhi 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