Elliptic curve cryptography (ecc) is an alternative to traditional techniques for public key cryptography it offers smaller key size without sacrificing security level tate pairing is a bilinear map used in identity based cryptography schemes. The elliptic curve scalar multiplication operation is performed by combining the elliptic curve point routines that are deﬁned in terms of the underlying ﬁnite ﬁeld arithmetic operations this thesis focuses on hardware architecture designs of elliptic curve operations. Elliptic curve cryptography (ecc) is an alternative to traditional techniques for public key cryptography it offers smaller key size without sacrificing security level.
A scalar multiplication in elliptic curve cryptography with binary polynomial operations in galois field thesis submitted to the faculty of computer science and information technology. Eﬃcient algorithms for finite fields, with applications in elliptic curve cryptography by sel¸cuk baktır a thesis submitted to the faculty of the. 1 introduction as the title suggests, this thesis is about elliptic curve cryptography an elliptic curve is a non-singular projective curve, given by a cubic equation over an arbitrary.
Elliptic curves and cryptography a thesis presented to the faculty of the department of mathematics san jos¶e state university in partial fulﬂllment. Alternative applications of elliptic curves and to make existing applications more e cient by arithmetic speedups in this master thesis we are going to discuss the elliptic curve only hash (ecoh), a hash algorithm based on elliptic curves, and edwards curves, a new curve shape having a fast and complete addition law. Elliptic curve cryptography on modern processor architectures neil costigan bsc, msc a thesis submitted for the degree of phd to the dublin city university. Colby college honors thesis a coder's guide to elliptic curve cryptography author: stephen morse supervisor: fernando gouveˆa a thesis submitted in fulﬁlment of the requirements. Abstract pairing-based cryptography has become a highly active research area we deﬁne bilinear maps, or pairings, and show how they give rise to cryptosystems with new functionality.
Applications of frobenius expansions in elliptic curve cryptography by waldyr dias benits junior¶ thesis submitted to the university of london for the degree of. Abstract elliptic curve cryptography (ecc) is a kind of public key cryptography founded in the theory of groups ecc's main advantage is the short length of the keys.
Cryptography phd thesis - didaonline cs 787 is a seminar-style course in which students will readand present papers on current research in cryptography potential topicsinclude zero knowledge, concurrency and protocol security, database privacy,connections between symbolic and computational security analysis, andcryptographic game theory. Elliptic curve cryptography has expanded the use of public-key cryptosystems, providing systems of encryption that are easier to implement and harder to crack  the graphs and tables for the examples in this paper were generated with the. Cryptography and elliptic curves this chapter provides an overview of the use of elliptic curves in cryptography we rst provide a brief background to public key cryptography and the discrete logarithm problem, before introducing elliptic curves and the elliptic curve analogue of the discrete logarithm problem.
Elliptic curves over finite fields, master's thesis, george mason university, may 1992 [zuc97] z uccherato , r new applications of elliptic curves and function fields in cryptography , phd thesis, university of waterloo, 1997. Low power elliptic curve cryptography by erdin˘c ozt urk a thesis submitted to the faculty of the worcester polytechnic institute in partial ful llment of the. Reconfigurable elliptic curve cryptography by aarti malik a thesis submitted in partial fulfillment of the requirements for the degree of master of science in.
Elliptic curve cryptography improving the pollard-rho algorithm since elliptic curve cryptography is a relatively new phenomenon, research is the thesis will. Elliptic curves can be defined over any field k the formal definition of an elliptic curve is a non-singular projective algebraic curve over k with genus 1 and endowed with a distinguished point defined over k. Fpga implementation for elliptic curve cryptography over binary extension field by che chen a thesis submitted to the faculty of graduate studies.