Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer factorization algorithm
|
| gptkbp:application |
crypt
RSA key testing |
| gptkbp:complexity |
sub-exponential (for some numbers)
|
| gptkbp:field |
cryptography
number theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Pollard's p−1 algorithm
|
| gptkbp:introducedIn |
1974
|
| gptkbp:inventedBy |
gptkb:John_Pollard
|
| gptkbp:limitation |
ineffective if all p−1 have large prime factors
|
| gptkbp:output |
nontrivial factor of n (if successful)
|
| gptkbp:purpose |
integer factorization
|
| gptkbp:relatedTo |
gptkb:Pollard's_rho_algorithm
gptkb:Fermat's_factorization_method |
| gptkbp:step |
choose a bound B
compute a^M mod n compute gcd(a^M - 1, n) |
| gptkbp:uses |
modular exponentiation
|
| gptkbp:worksWellFor |
numbers with a prime factor p such that p−1 is smooth
|
| gptkbp:bfsParent |
gptkb:Lenstra_elliptic-curve_factorization
|
| gptkbp:bfsLayer |
7
|