def encrypt(self, m, r=None):
if self.h is None:
raise ValueError("Public key not set.")
if r is None:
r = uniform_sample_T(self.N, self.d, self.d)
blind = Polynomial(self.p).__mul__(self.h.__mul__(r, self.q), self.q)
return (blind.__add__(m, self.q)).__mod__(self.poly_mod, self.q)
def cycle_index_sym_helper(n: int, memo: Dict[int, Polynomial]) -> Polynomial:
"""
A helper for the dp-style evaluation
of the cycle index.
The recurrence is given in:
https://en.wikipedia.org/wiki/Cycle_index#Symmetric_group_Sn
"""
if n in memo:
return memo[n]
ans = Polynomial([Monomial({}, Fraction(0, 1))])
for t in range(1, n + 1):
ans = ans.__add__(
Polynomial([Monomial({t: 1}, Fraction(1, 1))]) *
cycle_index_sym_helper(n - t, memo))
ans *= Fraction(1, n)
memo[n] = ans
return memo[n]
