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| author | Paul Jungeblut <paul.jungeblut@gmail.com> | 2016-10-15 23:30:44 +0200 |
|---|---|---|
| committer | Paul Jungeblut <paul.jungeblut@gmail.com> | 2016-10-15 23:30:44 +0200 |
| commit | 463e389ea499dcc26314196c014a85ee9b124847 (patch) | |
| tree | 64fc77a603df88c4d898fba452c60006194c818a /math/primitiveRoot.cpp | |
| parent | 53c8e56d8b0ee3b4374ab90630673b971ddf2710 (diff) | |
Adding primitive root and discrete logarithm.
Diffstat (limited to 'math/primitiveRoot.cpp')
| -rw-r--r-- | math/primitiveRoot.cpp | 23 |
1 files changed, 23 insertions, 0 deletions
diff --git a/math/primitiveRoot.cpp b/math/primitiveRoot.cpp new file mode 100644 index 0000000..3ad828d --- /dev/null +++ b/math/primitiveRoot.cpp @@ -0,0 +1,23 @@ +// Ist g Primitivwurzel modulo p. Teste zufällige g, um eine zu finden. +bool is_primitive(ll g, ll p) { + map<ll, int> facs; + factor(p - 1, facs); + for (auto &f : facs) + if (1 == powMod(g, (p - 1) / f.first, p)) return false; + return true; +} + +// Alternativ: Generator zum Finden. -1 falls keine existiert. +ll generator (ll p) { // Laufzeit: O(ans*log(phi(n))*log(n)) + map<ll, int> facs; + factor(n, facs); + ll phi = phi(p), n = phi; + + for (ll res = 2; res <= p; res++) { + bool ok = true; + for (auto &f : facs) + ok &= powMod(res, phi / f.first, p) != 1; + if (ok) return res; + } + return -1; +} |
