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...
متن کاملIsogenies and the Discrete Logarithm Problem on Jacobians of Genus 3 Hyperelliptic Curves
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...
متن کاملHyperelliptic Jacobians and Modular Representations
In [17] the author proved that in characteristic 0 the jacobian J(C) = J(Cf ) of a hyperelliptic curve C = Cf : y 2 = f(x) has only trivial endomorphisms over an algebraic closure Ka of the ground field K if the Galois group Gal(f) of the irreducible polynomial f ∈ K[x] is “very big”. Namely, if n = deg(f) ≥ 5 and Gal(f) is either the symmetric group Sn or the alternating group An then the ring...
متن کاملNon-supersingular Hyperelliptic Jacobians
In his previous papers [25, 26, 28] the author proved that in characteristic 6= 2 the jacobian J(C) of a hyperelliptic curve C : y = f(x) has only trivial endomorphisms over an algebraic closure Ka of the ground field K if the Galois group Gal(f) of the irreducible polynomial f(x) ∈ K[x] is either the symmetric group Sn or the alternating group An. Here n ≥ 9 is the degree of f . The goal of th...
متن کاملHyperelliptic Jacobians with Real Multiplication
Let K be a field of characteristic different from 2, and let f(x) be a sextic polynomial irreducible over K with no repeated roots, whose Galois group is A5. If the Jacobian of the hyperelliptic curve y = f(x) admits real multiplication over the ground field from an order of a real quadratic number field, then either its endomorphism algebra is this quadratic field or the Jacobian is supersingu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2018.07.025