10085

9315

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

دوازده، 85ص.: جدول، نمودار

ص.ع. به فارسي و انگليسي

رضا رضائيان فراشاهي

عمران احمدي درويشوند

30/2/94

محمدرضا هوشمند اصل، امير هاشمي

1396/09/27

كتابنامه

علوم رياضي

رياضي

ID9315

Four Dimensional Gallant Lambert Vanstone Scalar Multiplication Rasoul Ghafarian r ghafarian@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 Advisor Dr Omran Ahamdi Darvishvandi oahmadid@ipm ir 2010 MSC 05C15 53C42 Keywords cryptography elliptic curve scalar multiplication e cient endomorphism lattice AbstractElliptic curve cryptography ECC is an approach to public key cryptography based on the algebraicstructure of elliptic curves over nite elds In comparison with other cryptographic systems basedon nite elds ECC provides the same level of security with keys of smaller size Elliptic curves areapplicable for encryption digital signatures pseudo random generators and other tasks They arealso used in several integer factorization algorithms that have applications in cryptography such asLenstra elliptic curve factorization Discrete logarithm problem can be applied over the group of pointsof an elliptic curve de ned over a nited eld Elliptic curve cryptosystems are more approperiatefor using in systems with limited memory bandwidth and limited computational ability rather thanother public key cryptosystems The fundamental operation in computation of the elliptic curvescryptography systems is the problem of computing scalar multiplication of a point of the ellipticcurve Therefore researchers have been trying to nd new methods for increasing the speed of thiscomputation The basic methods are the double and add method window method and comb method In this theses we will introduce the GLV method of Gallant Lambert and Vanstone that is usedfor computing scalar multiplication of a point of prime order of the elliptic curve with an e cientendomorphism This is done by considering a two dimensional decomposition using the concepts oflattices and e cient endomorphisms The GLS method of Galbraith Lin and Scott is the extensionof the GLV method over a larger class of elliptic curves which are twists of GLV curves By combining

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عمران احمدي درويشوند

محمدرضا هوشمند اصل، امير هاشمي