Real Jacobian Elliptic Function Parametrizations for a Genuinely Asymmetric Biquadratic Curve
نویسنده
چکیده
We give real Jacobian elliptic function parametrizations for a genuinely asymmetric biquadratic curve where the variables and parameters are real.
منابع مشابه
Integrable mappings of the plane preserving biquadratic invariant curves II
We review recently introduced curve-dependent McMillan maps which are mappings of the plane that preserve biquadratic foliations. We show that they are measure preserving and thus integrable. We discuss the geometry of these maps including their fixed points and their stability. We consider the normal forms of symmetric and asymmetric biquadratic curves and the normal forms for their associated...
متن کاملOn the Nonexistence of Certain Curves of Genus Two
We prove that if q is a power of an odd prime then there is no genus-2 curve over Fq whose Jacobian has characteristic polynomial of Frobenius equal to x + (2 − 2q)x + q. Our proof uses the Brauer relations in a biquadratic extension of Q to show that every principally polarized abelian surface over Fq with the given characteristic polynomial splits over Fq2 as a product of polarized elliptic c...
متن کاملAn Efficient Threshold Verifiable Multi-Secret Sharing Scheme Using Generalized Jacobian of Elliptic Curves
In a (t,n)-threshold secret sharing scheme, a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together, but no group of fewer than t participants can do. In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme based on Shao and Cao, and the intractability of the elliptic curve discrete logar...
متن کاملAllan Adler Eisenstein and the Jacobians of Fermat Curves § 0
In this paper, we present evidence that Eisenstein knew something about the Jacobian varieties of Fermat curves, including the curve of degree 7. More precisely, we claim that Eisenstein had some way of knowing that certain differentials on a Fermat curve of degree 7 are reducible to elliptic differentials without explicitly reducing them. Our argument depends on a close examination of Gauss’s ...
متن کاملGeneralized Jacobian and Discrete Logarithm Problem on Elliptic Curves
Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...
متن کامل