arXiv subjects

Kirsten Eisentraeger

Publications and source records attributed to Kirsten Eisentraeger.

20 records · Page 2Linked to original sources

arXiv2003

Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation

We present an algorithm which speeds scalar multiplication on a general elliptic curve by an estimated 3.8 % to 8.5 % over the best known general methods when using affine coordinates. This is achieved by eliminating a field multiplication when we compute 2P+Q from given points P, Q on the curve. We give applications to simultaneous multiple scalar multiplication and to the Elliptic Curve Method of factorization. We show how this improvement together with another idea can speed the computation of the Weil and Tate pairings by up to 7.8 %.

math.NT↗

arXiv2002

Hilbert's Tenth Problem for algebraic function fields of characteristic 2

Let K be an algebraic function field of characteristic 2 with constant field C_K. Let C be the algebraic closure of a finite field in K. Assume that C has an extension of degree 2. Assume that there are elements u,x of K with u transcendental over C_K and x algebraic over C(u) and such that K=C_K(u,x). Then Hilbert's Tenth Problem over K is undecidable. Together with Shlapentokh's result for odd characteristic this implies that Hilbert's Tenth Problem for any such field K of finite characteristic is undecidable. In particular, Hilbert's Tenth Problem for any algebraic function field with finite constant field is undecidable.

math.NT↗