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A Subexponential Algorithm for Discrete Logarithms Over all Finite Fields
| Content Provider | Scilit |
|---|---|
| Author | Adleman, Leonard M. Demarrais, Jonathan |
| Copyright Year | 1993 |
| Description | There are numerous subexponential algorithms for computing discrete logarithms over certain classes of finite fields. However, there appears to be no published subexponential algorithm for computing discrete logarithms over all finite fields. We present such an algorithm and a heuristic argument that there exists a $c \in {\Re _{ > 0}}$ such that for all sufficiently large prime powers ${p^n}$, the algorithm computes discrete logarithms over ${\text {GF}}({p^n})$ within expected time: ${e^{c{{(\log ({p^n})\log \log ({p^n}))}^{1/2}}}}$. |
| Related Links | https://www.ams.org/mcom/1993-61-203/S0025-5718-1993-1225541-3/S0025-5718-1993-1225541-3.pdf |
| ISSN | 00255718 |
| e-ISSN | 10886842 |
| DOI | 10.2307/2152932 |
| Journal | Mathematics of Computation |
| Issue Number | 203 |
| Volume Number | 61 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1993-07-01 |
| Access Restriction | Open |
| Subject Keyword | Logic Discrete Logarithms Subexponential Algorithm Finite Text Prime Sufficiently |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Algebra and Number Theory Computational Mathematics |
