Since every quadratic residue modulo " N " has four square roots, the probability that the receiver learns " m " is 1 / 2.
32.
Here ? is the quadratic residue symbol modulo " D ", where " " D " is the discriminant of an imaginary quadratic field.
33.
However, if the Jacobi symbol is 1 but the denominator is not a prime, it does not necessarily follow that the numerator is a quadratic residue of the denominator.
34.
The first set is the biquadratic residues, the third set is the quadratic residues that are not quartic residues, and the second and fourth sets are the quadratic nonresidues.
35.
Or in other words, when p is a prime that is neither 2 nor 5, 5 is a quadratic residue modulo p iff p is 1 or 4 modulo 5.
36.
Recovering the private key \ chi from \ gamma is computationally infeasible, at least as hard as finding square roots mod " n " ( see quadratic residue ).
37.
In particular, the Kronecker symbol \ left ( \ tfrac an \ right ) for even n can take values independently on whether a is a quadratic residue or nonresidue modulo n.
38.
*PM : cases when minus one is a quadratic residue, id = 8424 new !-- WP guess : cases when minus one is a quadratic residue-- Status:
39.
*PM : cases when minus one is a quadratic residue, id = 8424 new !-- WP guess : cases when minus one is a quadratic residue-- Status:
40.
For a given " n " a list of the quadratic residues modulo " n " may be obtained by simply squaring the numbers 0, 1, &,.
