Isogenies of Jacobians
نویسندگان
چکیده
منابع مشابه
Families of Explicit Isogenies of Hyperelliptic Jacobians
We construct three-dimensional families of hyperelliptic curves of genus 6, 12, and 14, two-dimensional families of hyperelliptic curves of genus 3, 6, 7, 10, 20, and 30, and one-dimensional families of hyperelliptic curves of genus 5, 10 and 15, all of which are equipped with an an explicit isogeny from their Jacobian to another hyperelliptic Jacobian. We show that the Jacobians are genericall...
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In this paper, we compute `-isogenies between abelian varieties over a field of characteristic different from 2 in polynomial time in `, when ` is an odd prime which is coprime to the characteristic. We use level n symmetric theta structure where n = 2 or n = 4. In a second part of this paper we explain how to convert between Mumford coordinates of Jacobians of genus 2 hyperelliptic curves to t...
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We describe the use of explicit isogenies to reduce Discrete Logarithm Problems (DLPs) on Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperelliptic genus 3 curves, which are vulnerable to faster index calculus attacks. We provide algorithms which compute an isogeny with kernel isomorphic to (Z/2Z) for any hyperelliptic genus 3 curve. These algorithms provide a rational isogeny...
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In this paper, we compute `-isogenies between abelian varieties over a field of characteristic different from 2 in polynomial time in `, when ` is an odd prime which is coprime to the characteristic. We use level n symmetric theta structure where n = 2 or n = 4. In a second part of this paper we explain how to convert between Mumford coordinates of Jacobians of genus 2 hyperelliptic curves to t...
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ژورنال
عنوان ژورنال: Algebraic Geometry
سال: 2016
ISSN: 2214-2584
DOI: 10.14231/ag-2016-020