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D.12.2 atkins_lib

Procedures for teaching cryptography
Stefan Steidel, steidel@mathematik.uni-kl.de

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.


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