Algebraic Curves, Symmetries and Satellites

Algebraic Curves, Symmetries and Satellites.

Symmetries and similarities of planar algebraic curves using harmonic polynomials

We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a similarity transformation. Both algorithms are based on the fact, well-known in Harmonic Analysis, that the Laplacian operator commutes with orthogonal transformatio...

Symmetries of Curves and Surfaces

Algebraic Curves

We consider the problem of tracing algebraic curves by computer, using a numerical technique augmented by symbolic computations. In particular, all singularities are analyzed cOITectly. The methods presented find application in solid modeling and robotics.

Algebraic curves and cryptography

Algebraic curves over finite fields are being extensively used in the design of public-key cryptographic schemes. This paper surveys some topics in algebraic curve cryptography, with an emphasis on recent developments in algorithms for the elliptic and hyperelliptic curve discrete logarithm problems, and computational problems in pairing-based cryptography.