Raw differences
pairwise difference field
Chaos Communication Camp Workshop
Workshop / Installation / Performance
Kunst der Kurven
Kunst der Kurven (Art of Curves) is a mix between an installation, workshop and a performance dealing with the topic of visualisation, sonification and enactment of algebraic structures known under the name of Elliptic Curves (EC). ECs are fundamental for modern asymmetric cryptography, cryptocurrencies and related computational worlds, but for those who know these Abelian varieties better, they can also be regarded as beautiful structures on their own. Seemingly chaotic at first sight, ECs encode and exhibit certain symmetries which can be visualised – or even sonified – to produce results of non-negligible artistic and aesthetic value.
installation / workshop / performance
Quadratic character
difference matrix
Cubic character
difference matrix
Quadratic product
outer-product character field
Article
Publication
Canonical p-Adic n-Alignment of Elliptic Curve Points and Preservation of Unknown Scalar Relations
We give an explicit and computationally effective construction of a canonical p-adic lift of elliptic curve points of order prime to p. Given independently chosen p-adic lifts of points defined over a finite field, we describe an alignment procedure that forces all group-law relations-including unknown scalar relations-to hold in the p-adic setting. The construction relies on the rigidity of prime-top torsion, formal group theory, and good reduction. The alignment procedure yields the unique étale realization of the base-field elliptic curve group inside a high-precision p-adic coordinate space, eliminating all lift-dependent formal artifacts while preserving the full group structure.
text / theory