Then the signature s is computed by the signing function:
s = xe mod m
for a chosen signing exponent e and modulus m.
This function is private because e is known only to the author.
The modulus m must be public because it is used by the receiver of the
message in the verification function:
x = s3 mod m
This works because m and e are chosen in such a way that:
x = (xe mod m)3 mod m