The Construction Of Efficiently Computable Endomorphisms For Scalar Multiplication On Some Elliptic Curves

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dc.contributor.authorMohamad Anwar Antony, Siti Noor Farwina
dc.date.accessioned2020-03-11T08:08:57Z
dc.date.available2020-03-11T08:08:57Z
dc.date.issued2019-05
dc.description.abstractElliptic curves scalar multiplication (ECSM), denoted as kP, is one of the building blocks in Elliptic Curve Cryptography (ECC). An elliptic curve, E defined over a finite prime field, Fp have finitely many points which form an abelian group and there exists a prime subgroup with order n. ECSM involves the multiplication of scalar k 2 [1;n􀀀1] and a point P which belongs to the prime subgroup. ECSM consumes the highest operating cost in ECC which later affects the efficiency of this cryptosystem. For the past few years, many researchers proposed various methods, such as the Gallant, Lambert and Vanstone (GLV) method and Integer Sub-Decomposition (ISD) method, to reduce the operation cost of ECSM. One of the approaches to reduce the operation cost of ECSM is by employing an efficiently computable endomorphism. This research aims to construct efficiently computable endomorphisms on selected elliptic curves, mainly elliptic curves with j-invariant, j(E) = 0;1728;8000;54000, which corresponds to imaginary quadratic field Q( p 􀀀3);Q( p 􀀀1);Q( p 􀀀2); Q( p 􀀀3), with discriminant, D = 􀀀3;􀀀4;􀀀8;􀀀12, respectively. These imaginary quadratic fields correspond to a unique reduced form of prime numbers and a unique maximal order, respectively. The maximal order for each imaginary quadratic field satisfies a specific monic polynomial which becomes the characteristic polynomial for the endomorphisms that has been constructed to represent the complex multiplication on elliptic curves.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/9616
dc.language.isoenen_US
dc.publisherUniversiti Sains Malaysiaen_US
dc.subjectOf Efficiently Computable Endomorphismsen_US
dc.subjectElliptic Curvesen_US
dc.titleThe Construction Of Efficiently Computable Endomorphisms For Scalar Multiplication On Some Elliptic Curvesen_US
dc.typeThesisen_US
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