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
How a nonassociative algebra reflects the properties of a skew polynomial
Christian Brown,Susanne Pumpluen +1 more
TL;DR: In this article, the authors give necessary and sufficient criteria for skew polynomials of low degree to be irreducible, and give canonical examples of right division algebras when the right nucleus of a polynomial is chosen.
Hardware implementation of elliptic curve Diffie-Hellman key agreement scheme in GF(p)
Zerene Sangma
- 01 Jan 2008
TL;DR: This thesis examines various scalable implementations of elliptic curve scalar multiplication employing multiplicative inverse or field division in GF(p) focussing mainly on modular divison architectures and presents a new architecture for modular division based on the variant of Extended Binary GCD algorithm.
Design and Analysis of Efficient Parallel Hardware Prime Generators
TL;DR: An efficient hardware prime generator is presented that generates a prime p by combining trial division and Fermat test in parallel and probabilistic analysis is presented to determine the optimal k and to estimate the expected running time for the parallel combination.
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•Posted Content
Self-image effects in diffraction and dispersion
TL;DR: In this article, the wavelet transform was applied to the fractal Talbot effect in both diffraction and fiber dispersion, and the self-similar character of the transverse paraxial field at irrational multiples of the Talbot distance was confirmed, whereas the field is not self similar for supergaussian pulses.
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Extensions in the theory of Lucas and Lehmer pseudoprimes
Andrew David Loveless
- 01 Jan 2005
TL;DR: Loveless et al. as mentioned in this paper studied probabilistic primality testing based on Lucas and Lehmer sequences and gave four congruence relations for these sequences which are satisfied by all primes.
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.
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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.