1 
Canonical and minimal degree liftings of curvesFinotti, Luís Renato Abib, January 2001 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.

2 
Canonical and minimal degree liftings of curves /Finotti, Luis Renato Abib, January 2001 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 7273). Available also in a digital version from Dissertation Abstracts.

3 
Canonical and minimal degree liftings of curvesFinotti, Luís Renato Abib, 1973 14 March 2011 (has links)
Not available / text

4 
Rational points on elliptic curvesScarowsky, P. M. January 1969 (has links)
No description available.

5 
Rational points on elliptic curvesScarowsky, P. M. January 1969 (has links)
No description available.

6 
Algorithms in Elliptic Curve CryptographyUnknown Date (has links)
Elliptic curves have played a large role in modern cryptography. Most notably,
the Elliptic Curve Digital Signature Algorithm (ECDSA) and the Elliptic Curve
Di eHellman (ECDH) key exchange algorithm are widely used in practice today for
their e ciency and small key sizes. More recently, the Supersingular Isogenybased
Di eHellman (SIDH) algorithm provides a method of exchanging keys which is conjectured
to be secure in the postquantum setting. For ECDSA and ECDH, e cient
and secure algorithms for scalar multiplication of points are necessary for modern use
of these protocols. Likewise, in SIDH it is necessary to be able to compute an isogeny
from a given nite subgroup of an elliptic curve in a fast and secure fashion.
We therefore nd strong motivation to study and improve the algorithms used
in elliptic curve cryptography, and to develop new algorithms to be deployed within
these protocols. In this thesis we design and develop dMUL, a multidimensional
scalar multiplication algorithm which is uniform in its operations and generalizes the
well known 1dimensional Montgomery ladder addition chain and the 2dimensional
addition chain due to Dan J. Bernstein. We analyze the construction and derive many
optimizations, implement the algorithm in software, and prove many theoretical and practical results. In the nal chapter of the thesis we analyze the operations carried
out in the construction of an isogeny from a given subgroup, as performed in SIDH.
We detail how to e ciently make use of parallel processing when constructing this
isogeny. / Includes bibliography. / Dissertation (Ph.D.)Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

7 
A novel high speed GF (2173) elliptic curve cryptoprocessor.January 2003 (has links)
Leung Pak Keung. / Thesis (M.Phil.)Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 6970). / Abstracts in English and Chinese. / Chapter Chapter 1  Introduction  p.1 / Chapter 1.1  Introduction to Elliptic Curve Cryptoprocessor  p.1 / Chapter 1.2  Aims  p.2 / Chapter 1.3  Contributions  p.2 / Chapter 1.4  Thesis Outline  p.3 / Chapter Chapter 2  Cryptography  p.5 / Chapter 2.1  Introduction to Cryptography  p.5 / Chapter 2.2  Publickey Cryptosystems  p.6 / Chapter 2.3  Secretkey Cryptosystems  p.9 / Chapter 2.4  Discrete Logarithm Problem  p.9 / Chapter 2.5  Comparison between ECC and RSA  p.10 / Chapter 2.6  Summary  p.13 / Chapter Chapter 3  Mathematical Background in Number Systems  p.14 / Chapter 3.1  Introduction to Number Systems  p.14 / Chapter 3.2  "Groups, Rings and Fields"  p.14 / Chapter 3.3  Finite Fields  p.15 / Chapter 3.4  Modular Arithmetic  p.16 / Chapter 3.5  Optimal Normal Basis  p.16 / Chapter 3.5.1  What is a Normal Basis?  p.17 / Chapter 3.5.2  Addition  p.17 / Chapter 3.5.3  Squaring  p.18 / Chapter 3.5.4  Multiplication  p.19 / Chapter 3.5.5  Optimal Normal Basis  p.19 / Chapter 3.5.6  Generation of the Lambda Matrix  p.20 / Chapter 3.5.7  Inversion  p.22 / Chapter 3.6  Summary  p.24 / Chapter Chapter 4  Introduction to Elliptic Curve Mathematics  p.26 / Chapter 4.1  Introduction  p.26 / Chapter 4.2  Mathematical Background of Elliptic Curves  p.26 / Chapter 4.3  Elliptic Curve over Real Number System  p.27 / Chapter 4.3.1  Order of the Elliptic Curves  p.28 / Chapter 4.3.2  Negation of Point P  p.28 / Chapter 4.3.3  Point at Infinity  p.28 / Chapter 4.3.4  Elliptic Curve Addition  p.29 / Chapter 4.3.5  Elliptic Curve Doubling  p.30 / Chapter 4.3.6  Equations of Curve Addition and Curve Doubling  p.31 / Chapter 4.4  Elliptic Curve over Finite Fields Number System  p.32 / Chapter 4.4.1  Elliptic Curve Operations in Optimal Normal Basis Number System  p.32 / Chapter 4.4.2  Elliptic Curve Operations in Projective Coordinates  p.33 / Chapter 4.4.3  Elliptic Curve Equations in Projective Coordinates  p.34 / Chapter 4.5  Curve Multiplication  p.36 / Chapter 4.6  Elliptic Curve Discrete Logarithm Problem  p.37 / Chapter 4.7  Publickey Cryptography in Elliptic Curve Cryptosystem  p.38 / Chapter 4.8  DiffieHellman Key Exchange in Elliptic Curve Cryptosystem  p.38 / Chapter 4.9  Summary  p.39 / Chapter Chapter 5  Design Architecture  p.40 / Chapter 5.1  Introduction  p.40 / Chapter 5.2  Criteria for the Low Power System Design  p.40 / Chapter 5.3  Simplification in ONB Curve Addition Equations over Projective Coordinates  p.41 / Chapter 5.4  Finite Field Adder Architecture  p.43 / Chapter 5.5  Finite Field Squaring Architecture  p.43 / Chapter 5.6  Finite Field Multiplier Architecture  p.44 / Chapter 5.7  3way Parallel Finite Field Multiplier  p.46 / Chapter 5.8  Finite Field Arithmetic Logic Unit  p.47 / Chapter 5.9  Elliptic Curve Cryptoprocessor Control Unit  p.50 / Chapter 5.10  Register Unit  p.52 / Chapter 5.11  Summary  p.53 / Chapter Chapter 6  Specifications and Communication Protocol of the IC  p.54 / Chapter 6.1  Introduction  p.54 / Chapter 6.2  Specifications  p.54 / Chapter 6.3  Communication Protocol  p.57 / Chapter Chapter 7  Results  p.59 / Chapter 7.1  Introduction  p.59 / Chapter 7.2  Results of the Publickey Cryptography  p.59 / Chapter 7.3  Results of the Sessionkey Cryptography  p.62 / Chapter 7.4  Comparison with the Existing Cryptoprocessor  p.65 / Chapter 7.5  Power Consumption  p.66 / Chapter Chapter 8  Conclusion  p.68 / Bibliography  p.69 / Appendix  p.71 / 173bit Type II ONB Multiplication Table  p.71 / Layout View of the Elliptic Curve Cryptoprocessor  p.76 / Schematics of the Elliptic Curve Cryptoprocessor  p.77 / Schematics of the System Level Design  p.78 / Schematics of the I/O Control Interface  p.79 / Schematics of the Curve Multiplication Module  p.80 / Schematics of the Curve Addition Module  p.81 / Schematics of the Curve Doubling Module  p.82 / Schematics of the Field Inversion Module  p.83 / Schematics of the Register Unit  p.84 / Schematics of the Datapath  p.85 / Schematics of the Finite Field ALU  p.86 / Schematics of the 3way Parallel Multiplier  p.87 / Schematics of the Multiplier Elements  p.88 / Schematics of the Field Adder  p.89 / Schematics of Demultiplexer  p.90 / Schematics of the Control of the Demultiplexer  p.91

8 
Computer architectures for cryptosystems based on hyperelliptic curves.Wollinger, Thomas. January 2001 (has links)
Thesis (M.S.)Worcester Polytechnic Institute. / Keywords: binary field arithmetic, gcd, hardware architectures, polynomial arithmetic, cryptosystem, hyperelliptic curves. Includes bibliographical references (leaves 8287).

9 
Height functions on elliptic curves over function fields: a differentialgeometric approachChen, Cangxiong., 陈仓雄. January 2011 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy

10 
Genus 2 curves in pairingbased cryptography and the minimal embedding fieldHitt, Laura Michelle, 1979 29 August 2008 (has links)
Not available

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