Meletiou, Gerasimos C. Explicit form for the discrete logarithm over the field \(\text{GF}(p,k)\). (English) Zbl 0818.11049 Arch. Math., Brno 29, No. 1-2, 25-28 (1993). Let \(a\) be a primitive element for the field \(F= \text{GF} (p^ k)\). The purpose of this note is to give for each non-zero \(b\in F\) an explicit form of the integer \(z\) for which \(1\leq z\leq p^ k-1\), \(b= a^ z\). Writing \(z= \sum_{m=0}^{k-1} d_ m p^ m\), where \(0\leq d_ m\leq p-1\), he shows that \(d_ m= \sum_{i=1}^{q-2} b^ i/ (1+ a^ i)^{2^ m}\), \(0\leq m\leq k-1\). This is a straightforward generalization of the formula for \(d_ 0\) found by A. L. Wells [IEEE Trans. Inf. Theory IT-30, 845-846 (1984; Zbl 0558.12009)]. Reviewer: S.E.Payne (Denver) Cited in 6 Documents MSC: 11T71 Algebraic coding theory; cryptography (number-theoretic aspects) 11T99 Finite fields and commutative rings (number-theoretic aspects) 94A60 Cryptography Keywords:discrete logarithm; finite fields; cryptography; primitive element Citations:Zbl 0558.12009 × Cite Format Result Cite Review PDF Full Text: EuDML EMIS