Computational problems in supersingular elliptic curve isogenies
نویسندگان
چکیده
منابع مشابه
Computational problems in supersingular elliptic curve isogenies
We give a brief survey of elliptic curve isogenies and the computational problems relevant for supersingular isogeny crypto. Supersingular isogeny cryptography is attracting attention due to the fact that there are no quantum attacks known against it that are significantly faster than classical attacks. However, the underlying computational problems have not been sufficiently studied by quantum...
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Possibility of the emergence of quantum computers in the near future, pose a serious threat against the security of widely-used public key cryptosystems such as RSA or Elliptic Curve Cryptography (ECC). Algorithms involving isogeny computations on supersingular elliptic curves have been shown to be difficult to break, even to quantum computers. Thus, isogeny-based protocols represent promising ...
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In this paper, we describe a quantum algorithm for computing an isogeny between any two supersingular elliptic curves defined over a given finite field. The complexity of our method is in Õ(p) where p is the characteristic of the base field. Our method is an asymptotic improvement over the previous fastest known method which had complexity Õ(p) (on both classical and quantum computers). We also...
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In this paper we investigate stable operations in supersingular elliptic cohomology using isogenies of supersingular elliptic curves over nite elds. Our main results provide a framework in which we give a conceptually simple new proof of an elliptic cohomology version of the Morava change of rings theorem and also gives models for explicit stable operations in terms of isogenies and morphisms i...
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ژورنال
عنوان ژورنال: Quantum Information Processing
سال: 2018
ISSN: 1570-0755,1573-1332
DOI: 10.1007/s11128-018-2023-6