پديد آورنده :
دارابي، ساحل
عنوان :
محاسبات كارآمد روي خم هاي بيضوي
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان:دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
استاد راهنما :
رضا رضائيان فراشاهي
واژه نامه :
به فارسي و انگليسي
توصيفگر ها :
خم هاي ادواردز , خم هاي ادواردز پيچشي , فرمول هاي جمع و دوبرابر كردن , فرمول جمع كامل
تاريخ نمايه سازي :
1394/11/10
استاد داور :
عمران احمدي درويشوند، امير هاشمي
چكيده انگليسي :
E cient arithmetic on Edwards Curves Sahel Darabi sahel darabi@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Reza Rezaeian Farashahi farashahi@cc iut ac ir 2010 MSC 68P25 14G50 11T71 94A60 Keywords Elliptic curves Edwards curves Twisted edwards curves Addition and doubling law AbstractThe mathematics of elliptic curves has been studied for a decade in the elds of number theoryand arithmetic geometry The use of elliptic curves in cryptography was suggested independently byKoblitz and Miller in 1985 Since then many scientists have worked on elliptic curve cryptographyand have studied several subjects of this area of research Now a days the main important applicationof elliptic curves is in cryptography The traditional model to de ne an elliptic curve is the so called Weierstrass equation Over thelast 30 years many scientists have evaluated di erent forms of elliptic curves also have introducedseveral new forms and coordinate systems to improve the e ciency of elliptic curve cryptography In 2007 Edwards introduced a new normal form for elliptic curves and presented its additionlow Every elliptic curve over a non binary eld can be converted to a curve in Edwards form over anextension of the ground eld After the presentation of Edwards Bernstein and Lange observed theimpact of the proposed form in elliptic curve cryptography They extended this form and providedthe addition and doubling formulas improving the e ciency and speed The addition formulas areuni ed i e work for doubling Moreover for a subfamily of elliptic curves the addition formulashave the feature of completeness i e work for any pair of points without exception The proposedform is known as the Edwards form Latter on Bernstein et al suggested the inverted Edwards coordinates to improve the speed ofthe point addition computation Furthermore they extended the family of Edwards to the family oftwisted Edwards curves to cover more isomorphism classes of elliptic curves over the ground nite eld There is a one to one correspondence between the twisted Edwards curves and Montgomery
استاد راهنما :
رضا رضائيان فراشاهي
استاد داور :
عمران احمدي درويشوند، امير هاشمي
