Isogeny cordillera algorithm to obtain cryptographically good elliptic curves
نویسندگان
چکیده
The security of most elliptic curve cryptosystems is based on the intractability of the Elliptic Curve Discrete Logarithm Problem (ECDLP). Such a problem turns out to be computationally unfeasible when elliptic curves are suitably chosen. This paper provides an algorithm to obtain cryptographically good elliptic curves from a given one. The core of such a procedure lies on the usage of successive chains of isogenies, visiting different volcanoes of isogenies which are located in different `–cordilleras.
منابع مشابه
Exploiting Isogeny Cordillera Structure to Obtain Cryptographically Good Elliptic Curves
The security of most elliptic curve cryptosystems is based on the intractability of the Elliptic Curve Discrete Logarithm Problem (ECDLP). Such a problem turns out to be computationally unfeasible when elliptic curves are suitably chosen. This paper provides an algorithm to obtain cryptographically good elliptic curves from a given one. The core of such a procedure lies on the usage of successi...
متن کاملE cient Scalar Multiplication by Isogeny Decompositions
On an elliptic curve, the degree of an isogeny corresponds essentially to the degrees of the polynomial expressions involved in its application. The multiplication by ` map [`] has degree `, therefore the complexity to directly evaluate [`](P ) is O(`). For a small prime ` (= 2, 3) such that the additive binary representation provides no better performance, this represents the true cost of appl...
متن کاملAn AGM-type elliptic curve point counting algorithm in characteristic three
Given an ordinary elliptic curve on Hesse form over a finite field of characteristic three, we give a sequence of elliptic curves which leads to an effective construction of the canonical lift, and obtain an algorithm for computing the number of points. Our methods are based on the study of an explicitly and naturally given 3-isogeny between elliptic curves on Hesse form.
متن کاملConstructing elliptic curve isogenies in quantum subexponential time
Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to be computationally difficult. The fastest known classical algorithm takes exponential time, and prior to our work no faster quantum algorithm was known. Recently, public-key cryptosystems based on t...
متن کاملEfficient Scalar Multiplication by Isogeny Decompositions
On an elliptic curve, the degree of an isogeny corresponds essentially to the degrees of the polynomial expressions involved in its application. The multiplication–by– map [ ] has degree , therefore the complexity to directly evaluate [ ](P ) is O( ). For a small prime (= 2, 3) such that the additive binary representation provides no better performance, this represents the true cost of applicat...
متن کامل