Discrete Log Solver
One group per line: g,h,p separated by comma or space, e.g. 5,8,23 means solve 5^x = 8 (mod 23)
Method:
Solutions:
Formula:
Order of g:
Max results:
Max m digits:
Separator:
Calculation Result
Download CSV
| No. | Input (g,h,p) | Method | Solution x | Verify | Steps | Note |
|---|
Introduction to the tool and how to use it
Online discrete logarithm solver: find the exponent x in g^x ≡ h (mod p); enter one g,h,p triple per line to solve in batch.
Input format: one g,h,p triple per line, comma or space separated; for example
Three algorithms: BSGS (baby-step giant-step, default; build a baby table with m = ⌈√n⌉ and collide giant steps), brute force (for small p, with an iteration cap), Pohlig–Hellman (when p-1 is smooth; factor n into prime powers and combine by CRT); choose compare all to see the step counts of all three at once.
Automatic checks: if g's order is not entered, it is detected automatically; the tool checks whether g and p are coprime and whether p is prime, and uses h^n ≡ 1 to decide whether h lies in the subgroup generated by g; if not, it clearly reports no solution within the given range.
Verification: every computed x is rechecked with g^x mod p = h, and the verification column shows pass or fail; optionally output all solutions x + k·n. All big-number arithmetic uses BigInt with fast exponentiation throughout, and p holds at most 120 digits.
Input format: one g,h,p triple per line, comma or space separated; for example
5,8,23 asks for 5^x ≡ 8 (mod 23).Three algorithms: BSGS (baby-step giant-step, default; build a baby table with m = ⌈√n⌉ and collide giant steps), brute force (for small p, with an iteration cap), Pohlig–Hellman (when p-1 is smooth; factor n into prime powers and combine by CRT); choose compare all to see the step counts of all three at once.
Automatic checks: if g's order is not entered, it is detected automatically; the tool checks whether g and p are coprime and whether p is prime, and uses h^n ≡ 1 to decide whether h lies in the subgroup generated by g; if not, it clearly reports no solution within the given range.
Verification: every computed x is rechecked with g^x mod p = h, and the verification column shows pass or fail; optionally output all solutions x + k·n. All big-number arithmetic uses BigInt with fast exponentiation throughout, and p holds at most 120 digits.
How to use
- Paste each equation in g,h,p format, one per line.
- Choose the solving method, solution form, and other parameters.
- Click Run.
- Copy or export the solution x and the verification result.
Message board
All messages →-
No one has spoken up yet — want to go first?