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A cryptographic system is described which is secure if and only if computing logarithms over GF (p) is infeasible. Previously published algorithms for computing this function require O (p^1/2) complexity in both time and space. An improved algorithm is derived which requires O = (^2 p) complexity if p - 1 has only small prime factors. Such values of p must be avoided in the cryptosystem. Constructive uses for the new algorithm are also described.
Pohlig et al. (Sun,) studied this question.
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