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An improved algorithm for computing logarithms over GF(p) and its cryptographic significance (Corresp.)

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2 Author(s)

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 =(\log ^{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.

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Information Theory, IEEE Transactions on  (Volume:24 ,  Issue: 1 )