Rozprawy doktorskie na temat „Genus 2 curves”
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Flynn, Eugene Victor. "Curves of genus 2". Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305382.
Pełny tekst źródłaBending, Peter Richard. "Curves of genus 2 with #square root# 2 multiplication". Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267935.
Pełny tekst źródłaHanselman, Jeroen [Verfasser]. "Gluing curves of genus 2 and genus 1 along their 2-torsion / Jeroen Hanselman". Ulm : Universität Ulm, 2020. http://d-nb.info/1219964816/34.
Pełny tekst źródłaRedmond, Joanne. "Coverings of families of curves of genus 2". Thesis, University of Liverpool, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.250416.
Pełny tekst źródłaMaistret, Céline. "Parity of ranks of Jacobians of hyperelliptic curves of genus 2". Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/93324/.
Pełny tekst źródłaWilson, J. "Curves of genus 2 with real multiplication by a square root of 5". Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268031.
Pełny tekst źródłaChow, Rudolf Wing Tat. "The arithmetic-geometric mean and periods of curves of Genus 1 and 2". Thesis, University of Sheffield, 2018. http://etheses.whiterose.ac.uk/20887/.
Pełny tekst źródłaMoulahi, Samir. "Pinceaux réels en courbes de genre 2". Thesis, Angers, 2015. http://www.theses.fr/2015ANGE0022/document.
Pełny tekst źródłaLet π : X→ D be a real pencil of curves of genus two. The goal of this thesis is to give a partial classification of possible singular fibers; we give the types of real configurations of singular fibers and we determine the topology of neighbors fibers. Also we give the invariants determining in a unique way the real class of such pencils
Costello, Craig. "Fast formulas for computing cryptographic pairings". Thesis, Queensland University of Technology, 2012. https://eprints.qut.edu.au/61037/1/Craig_Costello_Thesis.pdf.
Pełny tekst źródłaGuillevic, Aurore. "Étude de l'arithmétique des couplages sur les courbes algébriques pour la cryptographie". Paris, Ecole normale supérieure, 2013. https://theses.hal.science/tel-00921940v1.
Pełny tekst źródłaSince 2000 pairings became a very useful tool to design new protocols in cryptography. Short signatures and identity-based encryption became also practical thanks to these pairings. This thesis contains two parts. One part is about optimized pairing implementation on different ellip- tic curves according to the targeted protocol. Pairings are implemented on supersingular elliptic curves in large characteristic and on Barreto-Naehrig curves. The pairing library developed at Thales is used in a broadcast encryption scheme prototype. The prototype implements pairings over Barreto-Naehrig curves. Pairings over supersingular curves are much slower and have larger parameters. However these curves are interesting when implementing protocols which use composite-order elliptic curves (the group order is an RSA modulus). We implement two protocols that use pairings on composite-order groups and compare the benchmarks and the parameter size with their counterpart in a prime-order setting. The composite-order case is 30 up to 250 times much slower according to the considered step in the protocols: the efficiency difference in between the two cases is very important. A second part in this thesis is about two families of genus 2 curves. Their Jacobians are isogenous to the product of two elliptic curves over a small extension field. The properties of elliptic curves can be translated to the Jacobians thanks to this isogeny. Point counting is as easy as for elliptic curves in this case. We also construct two endomorphisms both on the Jacobians and the elliptic curves. These en- domorphisms can be used for scalar multiplication improved with a four-dimensional Gallant-Lambert- Vanstone method
Balamohan, Balasingham. "Accelerating the scalar multiplication on genus 2 hyperelliptic curve cryptosystems". Thesis, University of Ottawa (Canada), 2010. http://hdl.handle.net/10393/28379.
Pełny tekst źródłaArène, Christophe. "Géométrie et arithmétique explicites des variétés abéliennes et applications à la cryptographie". Thesis, Aix-Marseille 2, 2011. http://www.theses.fr/2011AIX22069/document.
Pełny tekst źródłaThe main objects we study in this PhD thesis are the equations describing the group morphism on an abelian variety, embedded in a projective space, and their applications in cryptograhy. We denote by g its dimension and k its field of definition. This thesis is built in two parts. The first one is concerned by the study of Edwards curves, a model for elliptic curves having a cyclic subgroup of k-rational points of order 4, known in cryptography for the efficiency of their addition law and the fact that it can be defined for any couple of k-rational points (k-complete addition law). We give the corresponding geometric interpretation and deduce explicit formulae to calculate the reduced Tate pairing on twisted Edwards curves, whose efficiency compete with currently used elliptic models. The part ends with the generation, specific to pairing computation, of Edwards curves with today's cryptographic standard sizes. In the second part, we are interested in the notion of completeness introduced above. This property is cryptographically significant, indeed it permits to avoid physical attacks as side channel attacks, on elliptic -- or hyperelliptic -- curves cryptosystems. A preceeding work of Lange and Ruppert, based on cohomology of line bundles, brings a theoretic approach of addition laws. We present three important results: first of all we generalize a result of Bosma and Lenstra by proving that the group morphism can not be described by less than g+1 addition laws on the algebraic closure of k. Next, we prove that if the absolute Galois group of k is infinite, then any abelian variety can be projectively embedded together with a k-complete addition law. Moreover, a cryptographic use of abelian varieties restricting us to the dimension one and two cases, we prove that such a law exists for their classical projective embedding. Finally, we develop an algorithm, based on the theory of theta functions, computing this addition law in P^15 on the Jacobian of a genus two curve given in Rosenhain form. It is now included in AVIsogenies, a Magma package
CHOU, KUO MING JAMES. "Constructing pairing-friendly algebraic curves of genus 2 curves with small rho-value". Thesis, 2011. http://hdl.handle.net/1974/6866.
Pełny tekst źródłaThesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2011-11-08 18:57:59.988
Hitt, Laura Michelle 1979. "Genus 2 curves in pairing-based cryptography and the minimal embedding field". Thesis, 2007. http://hdl.handle.net/2152/3780.
Pełny tekst źródłaSadanandan, Sandeep [Verfasser]. "Counting in the Jacobian of hyperelliptic curves : in the light of genus 2 curves for cryptography / Sandeep Sadanandan". 2010. http://d-nb.info/1009379100/34.
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