Abstract:We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can be solved in the field of cardinality $p^n$ in expected time $(pn)^{2\log _2(n) + O(1)}$.

---

中文翻译：

---

固定特征有限域中拟多项式时间的离散对数

摘要：我们证明了离散对数问题可以在具有固定特征的有限域的乘法群中的拟多项式期望时间内求解。更一般地，我们证明它可以在基数 $p^n$ 领域中在期望时间 $(pn)^{2\log _2(n) + O(1)}$ 内求解。

---