During the construction of the PairingGroup:

• Check whether the secparam passed is valid.

For the method messageSize that computes the size of a message:

• Given that:
  • All the security parameters are positive integers (limited by the modification above);
  • Byte alignment is required, that is, after filling several bytes, any remaining one or more bits will occupy an additional byte, even if they do not form a complete byte;
  • $1, 2, \cdots, 8$ bit(s) occurpy $1$ byte, $9, 10, \cdots, 16$ bits occurpy $2$ bytes, $\cdots$; and
  • Issue Passing non-positive-integer secparam in PairingGroup construction #312 suggested bitwise operations, which is faster than ceil and /.
• We modify return self.secparam >> 3 to return (self.secparam + 1) >> 3

Additionally, it is also OK to only accept $\lambda$ that meets $8 | \lambda$, from my perspective. After importing ceil from math and making the ceil a local variable, ceil(self.secparam / 8) can faster than (self.secparam + 1) >> 3 only when the computation is used multiple times within the function. For example,

from math import ceil

def func():
    c = ceil
    for i in range(100000000):
        c(i / 8)

is faster than

def func():
    for i in range(100000000):
        (i + 7) >> 3

. However, in this situation, the computation of the message size is only used once in the method messageSize. Thus, we prefer to use return (self.secparam + 1) >> 3, which is faster than return ceil(self.secparam / 8).

Thank you for your consideration of this pull request to enhance the previous PR #314.