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High-performance Implementation of Elliptic Curve Cryptography Using Vector Instructions
ACM Transactions on Mathematical Software, 2019Elliptic curve cryptosystems are considered an efficient alternative to conventional systems such as DSA and RSA. Recently, Montgomery and Edwards elliptic curves have been used to implement cryptosystems.
Armando Faz-Hernández +2 more
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Quantum Resource Estimates for Computing Elliptic Curve Discrete Logarithms
International Conference on the Theory and Application of Cryptology and Information Security, 2017We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point addition ...
M. Rötteler +3 more
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American Journal of Mathematics, 1931
Zwei ebene Kurven heißen perspektiv, wenn zwischen den Punkten der ersten und den Tangenten der zweiten eine \((1,1)\)-Korrespondenz derart hergestellt werden kann, daß jede Tangente der zweiten durch den entsprechenden Punkt der ersten läuft. So sind z. B.
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Zwei ebene Kurven heißen perspektiv, wenn zwischen den Punkten der ersten und den Tangenten der zweiten eine \((1,1)\)-Korrespondenz derart hergestellt werden kann, daß jede Tangente der zweiten durch den entsprechenden Punkt der ersten läuft. So sind z. B.
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2008
Abstract The congruent number problem. A congruent numberis a rational number qthat is the area of a right triangle, all of whose sides have rational length. We observe that if the triangle has sides a, b, and c, and if sis a rational number, then s2qis also a congruent number whose associated triangle has sides sa, sb,and sc.So it is ...
G H Hardy, E . M Wright
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Abstract The congruent number problem. A congruent numberis a rational number qthat is the area of a right triangle, all of whose sides have rational length. We observe that if the triangle has sides a, b, and c, and if sis a rational number, then s2qis also a congruent number whose associated triangle has sides sa, sb,and sc.So it is ...
G H Hardy, E . M Wright
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The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book, reissued with a new Foreword, presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more modern developments.
Henry McKean, Victor Moll, Alex Kasman
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Henry McKean, Victor Moll, Alex Kasman
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The State of Elliptic Curve Cryptography
Des. Codes Cryptogr., 2000N. Koblitz, A. Menezes, S. Vanstone
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The Elliptic Curve Digital Signature Algorithm (ECDSA)
International Journal of Information Security, 2001D. Johnson, A. Menezes, S. Vanstone
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A novel image encryption scheme based on an elliptic curve
Signal Processing, 2019Umar Hayat, Naveed Ahmed Azam
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