Efficient solution of rational conics

Efficient solution of rational conics

We present efficient algorithms for solving Legendre equations over Q (equivalently, for finding rational points on rational conics) and parametrizing all solutions. Unlike existing algorithms, no integer factorization is required, provided that the prime factors of the discriminant are known.

Eecient Solution of Rational Conics

Efficient Solution of Rational

We present eecient algorithms for solving Legendre equations over Q (equivalently, for nding rational points on rational conics) and parametriz-ing all solutions. Unlike existing algorithms, no integer factorization is required , provided that the prime factors of the discriminant are known.

Rational Families of Conics and Quadrics

A surface generated by a one parameter family of conics c(t) is called conic surface. If c(t) can be described by rational functions, the generated conic surface is rational. An algorithm to construct real rational parametrizations for such surfaces and some examples will be given.

An efficient and secure RSA-like cryptosystem exploiting Rédei rational functions over conics

We define an isomorphism between the group of points of a conic and the set of integers modulo a prime equipped with a non-standard product. This product can be efficiently evaluated through the use of Rédei rational functions. We then exploit the isomorphism to construct a novel RSA-like scheme. We compare our scheme with classic RSA and with RSA-like schemes based on the cubic or conic equati...