def listRandomECs(m, irred, n):
if (m & (m-1)) != 0: # only powers of 2 don't have this property
return "" + str(m) + " is not a power of 2."
count = 0
rval = ""
deg = int(math.log(m, 2))
while count < n:
a = Polynomial.random(deg-1)
b = Polynomial.random(deg-1)
E = BinaryEllipticCurve(a, b, irred)
if E.isEC():
rval += str(E) + "\n"
count += 1
rval += str(count) + " curves were generated.\n"
return rval
def listRandomPoints(self, n):
count = 0
s = ""
a = self.getA()
b = self.getB()
modulus = self.getModulus()
deg = modulus.degree()
while count < n:
foundPoint = False
while not foundPoint:
x = Polynomial.random(deg-1)
y = Polynomial.random(deg-1)
leftside = (y*y + x*y) % modulus
rightside = (x*x*x + a*x*x + b) % modulus
if leftside == rightside:
foundPoint = True
s += str(PolynomialPoint(x, y, Polynomial("1"))) + "\n"
count += 1
s += str(count) + " points were generated.\n"
return s
