Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
Random number generation
Hash functions Pseudorandom generators Public-key cryptosystems |
| gptkbp:definedIn |
Integers congruent to a perfect square modulo n
|
| https://www.w3.org/2000/01/rdf-schema#label |
Quadratic residues
|
| gptkbp:opposedBy |
Quadratic nonresidues
|
| gptkbp:property |
0 is always a quadratic residue modulo n
1 is always a quadratic residue modulo n For an odd prime p, there are (p-1)/2 quadratic residues modulo p If x is a quadratic residue modulo n, then there exists y such that y^2 ≡ x (mod n) |
| gptkbp:relatedTo |
gptkb:Modular_arithmetic
gptkb:Multiplicative_group_modulo_n gptkb:Number_theory gptkb:Euler's_criterion gptkb:Tonelli–Shanks_algorithm Finite fields |
| gptkbp:studiedBy |
gptkb:Carl_Friedrich_Gauss
|
| gptkbp:symbol |
gptkb:Legendre_symbol
Jacobi symbol |
| gptkbp:usedIn |
gptkb:Quadratic_reciprocity
gptkb:Algebraic_number_theory Cryptography Primality testing |
| gptkbp:bfsParent |
gptkb:Quadratic_reciprocity
|
| gptkbp:bfsLayer |
6
|