Singular

D.12.2 atkins_lib

Library:

atkins.lib

Purpose:

Procedures for teaching cryptography

Author:

Stefan Steidel, steidel@mathematik.uni-kl.de

Note:

The library contains auxiliary procedures to compute the elliptic curve primality test of Atkin and the Atkin's Test itself. The library is intended to be used for teaching purposes but not for serious computations. Sufficiently high printlevel allows to control each step, thus illustrating the algorithms at work.

Procedures:

D.12.2.1 newTest		checks if number D already exists in list L
D.12.2.2 bubblesort		sorts elements of the list L
D.12.2.3 disc		generates a list of negative discriminants
D.12.2.4 Cornacchia		computes solution (x,y) for x^2+d*y^2=p
D.12.2.5 CornacchiaModified		computes solution (x,y) for x^2+|D|*y^2=4p
D.12.2.6 maximum		computes the maximal number contained in L
D.12.2.7 sqr		computes the square root of w w.r.t. accuracy k
D.12.2.8 expo		computes exp(z)
D.12.2.9 jOft		computes the j-invariant of t
D.12.2.10 round		rounds r to the nearest number out of Z
D.12.2.11 HilbertClassPoly		computes the Hilbert Class Polynomial
D.12.2.12 rootsModp		computes roots of the polynomial P modulo p
D.12.2.13 wUnit		computes the number of units in Q(sqr(D))
D.12.2.14 Atkin		tries to prove that N is prime