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Building cryptographic schemes based on elliptic curves over rational numbers
Научно-технический вестник информационных технологий, механики и оптикиThe possibility of using elliptic curves over the rational field of non-zero ranks in cryptographic schemes is studied. For the first time, the construction of cryptosystems is proposed the security of which is based on the complexity of solving the ...
V. V. Davydov +3 more
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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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Journal of the Mathematical Society of Japan, 2002 A remark is added. (after replace mistake).
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A generalized framework for elliptic curves based PRNG and its utilization in image encryption. [PDF]
Sci Rep, 2022 AbdElHaleem SH +2 more
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On isogenies of elliptic curves
Glasnik matematički, 2000 We give a characterization of ellptic curves which are isogenous over two different quadratic extensions of a fixed number field.
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Computing all integer solutions of a genus 1 equation [PDF]
The Elliptic Logarithm Method has been applied with great successto the problem of computing all integer solutions of equations ofdegree 3 and 4 defining elliptic curves. We extend this methodto include any equation f(u,v)=0 that defines a curve of genus
Stroeker, R.J., Tzanakis, N.
core
Algebraic curves, integer sequences and a discrete Painleve transcendent [PDF]
We consider some bilinear recurrences that have applications in number theory. The explicit solution of a general three-term bilinear recurrence relation of fourth order is given in terms of the Weierstrass sigma function for an associated elliptic curve.
Hone, Andrew N.W.
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Weyl groups and elliptic solutions of the WDVV equations [PDF]
, 2010 A functional ansatz is developed which gives certain elliptic solutions of the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations. This ansatz is based on the elliptic trilogarithm function introduced by Beilinson and Levin. For this to be a solution
Ian A. B. Strachan, Strachan, I.A.B.
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Secure elliptic curves in cryptography [PDF]
, 2017 Elliptic Curve Cryptography (ECC) is a branch of public-key cryptography based on the arithmetic of elliptic curves. In the short life of ECC, most standards have proposed curves defined over prime finite fields using the short Weierstrass form. However,
Lorena González-Manzano +5 more
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