Results 31 to 40 of about 568 (60)
, 2016 We revisit the mathematics that Ramanujan developed in connection with the famous "taxi-cab" number $1729$. A study of his writings reveals that he had been studying Euler's diophantine equation $$ a^3+b^3=c^3+d^3.
Ono, Ken, Trebat-Leder, Sarah
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Constructing elliptic curves of prime order [PDF]
, 2007 We present a very efficient algorithm to construct an elliptic curve E and a finite field F such that the order of the point group E(F) is a given prime number N.
Broker, Reinier, Stevenhagen, Peter
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Generating pairing-friendly elliptic curve parameters using sparse families
Journal of Mathematical Cryptology, 2018 The majority of methods for constructing pairing-friendly elliptic curves are based on representing the curve parameters as polynomial families. There are three such types, namely complete, complete with variable discriminant and sparse families. In this
Fotiadis Georgios, Konstantinou Elisavet
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Character sums with division polynomials
, 2011 We obtain nontrivial estimates of quadratic character sums of division polynomials $\Psi_n(P)$, $n=1,2, ...$, evaluated at a given point $P$ on an elliptic curve over a finite field of $q$ elements.
Igor E. Shparlinski +5 more
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Journal of Mathematical Cryptology, 2015 In this paper we present a new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves with small rho-values, and we improve on previously known best rho-values of families [J.
Yoon Kisoon
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COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES
Forum of Mathematics, Sigma, 2016 Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$
ANDREW V. SUTHERLAND
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The dihedral hidden subgroup problem
Journal of Mathematical CryptologyThe hidden subgroup problem (HSP) is a cornerstone problem in quantum computing, which captures many problems of interest and provides a standard framework algorithm for their study based on Fourier sampling, one class of techniques known to provide ...
Chen Imin, Sun David
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Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average
, 2007 We prove that the set of Farey fractions of order $T$, that is, the set $\{\alpha/\beta \in \Q : \gcd(\alpha, \beta) = 1, 1 \le \alpha, \beta \le T\}$, is uniformly distributed in residue classes modulo a prime $p$ provided $T \ge p^{1/2 +\eps}$ for any ...
Cojocaru, A. C., Shparlinski, I. E.
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Tate-Shafarevich Groups and Frobenius Fields of Reductions of Elliptic Curves [PDF]
, 2007 Let $\E/\Q$ be a fixed elliptic curve over $\Q$ which does not have complex multiplication. Assuming the Generalized Riemann Hypothesis, A. C. Cojocaru and W.
Shparlinski, Igor E.
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Modular Invariant of Quantum Tori II: The Golden Mean [PDF]
, 2012 In our first article in this series ("Modular Invariant of Quantum Tori I: Definitions Nonstandard and Standard" arXiv:0909.0143) a modular invariant of quantum tori was defined.
Bernard, C. Castaño, Gendron, T. M.
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