Open AccessBook
A Course in Number Theory and Cryptography
Neal Koblitz
- 01 Jan 1987
1.1K
TL;DR: Some topics in Elementary Number Theory include Finite Fields and Quadratic Residues, Primality and Factoring, and Elliptic Curves.
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Abstract: 1: Some Topics in Elementary Number Theory. 2: Finite Fields and Quadratic Residues. 3: Cryptography. 4: Public Key. 5: Primality and Factoring. 6: Elliptic Curves.
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Citations
A New Integration Scheme of Robust and Fragile for Secured Digital Watermarking
Lin Zhang,Fengyong Qian,Yi Gao,Yuesheng Zhu +3 more
- 03 Aug 2008
TL;DR: The results have shown that the proposed scheme can resist white noise, cropping, median filter and JPEG compressing distortions, and can be used for image verification and identity authentication.
2
Some computational problems motivated by the Birch and Swinnerton -Dyer conjecture
Iftikhar A. Burhanuddin
- 01 Jan 2007
TL;DR: The BSD conjecture for elliptic curves defined over the rational numbers has been open for over forty years and one of the seven Millennium Prize problems as mentioned in this paper, and it has been shown that there are infinitely many elliptic surfaces with Shafarevich-Tate group of size about
2
A mathematical model of the cryptosystem based on the linear Diophantine equation
V. O. Osipyan,K. I. Litvinov +1 more
- 10 Sep 2018
TL;DR: Cryptanalysis of described mathematical model demonstrates the potential of using Diophantine equations for the development of Information security systems despite the existing vulnerabilities.
2
A new blind identity-based signature scheme
Hassan M. Elkamchouchi,Yasmine Abouelseoud +1 more
- 01 Nov 2007
TL;DR: A new blind identity-based signature scheme based on bilinear pairings on elliptic curves is presented, which enables utilizing smaller key sizes, while achieving the same level of security compared to other schemes not utilizing elliptic curve.
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References
•Book
Introduction to Elliptic Curves and Modular Forms
Neal Koblitz
- 01 Jan 1984
TL;DR: The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory as discussed by the authors, and the current state of knowledge of ellipses.
1.2K
Factoring integers with elliptic curves
TL;DR: This paper is devoted to the description and analysis of a new algorithm to factor positive integers that depends on the use of elliptic curves and it is conjectured that the algorithm determines a non-trivial divisor of a composite number n in expected time at most K( p)(log n)2.
•Journal Article
Primitive points on elliptic curves
Rajiv Gupta,M. Ram Murty +1 more
TL;DR: In this article, the conditions générales d'utilisation (http://www.compositio.org/conditions) of the agreement with the Foundation Compositio Mathematica are defined.
Why Study Equations over Finite Fields
TL;DR: Finite field solutions to equations are related in a subtle and intriguing way to rational solutions and complex solutions as mentioned in this paper, and they are related to complex solutions in the sense that rational solutions are more complex than complex solutions.
7
Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
TL;DR: A deterministic algorithm to compute the number of F^-points of an elliptic curve that is defined over a finite field Fv and which is given by a Weierstrass equation is presented.