def __invert__(self):
'''Inversion modulo order (redefinition of operator '~')
@note: This method caches modular inverse, so modifying value of X
directly with 'X.value = ...' can lead to incoherent inversion.
'''
if self.inverse == None: # caching inverse value (speed optimization)
self.inverse = PrimeField(modinv(self.value, self.order),
self.order)
return self.inverse
def __invert__(self):
'''Inversion (redefinition of operator '~')
If [A(x) * B(x) mod P(x)=x^2+1] == 1, then computes
B(x) for a given A(x).
Direct inversion algorithm
'''
delta = self.value[1] ** 2 + self.value[0] ** 2
deltaInv = modinv(delta, self.order)
return PrimeField2([(-self.value[0]) * deltaInv,
self.value[1] * deltaInv],
self.order)
