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Index calculus algorithm
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==History== The basic idea of the algorithm is due to Western and Miller (1968),<ref>Western and Miller (1968) ''Tables of indices and primitive roots'', Royal Society Mathematical Tables, vol 9, Cambridge University Press.</ref> which ultimately relies on ideas from Kraitchik (1922).<ref>M. Kraitchik, ''Théorie des nombres'', Gauthier--Villards, 1922</ref> The first practical implementations followed the 1976 introduction of the [[Diffie-Hellman]] cryptosystem which relies on the discrete logarithm. Merkle's Stanford University dissertation (1979) was credited by Pohlig (1977) and Hellman and Reyneri (1983), who also made improvements to the implementation.<ref>Pohlig, S. ''Algebraic and combinatoric aspects of cryptography''. Tech. Rep. No. 6602-1, Stanford Electron. Labs., Stanford, Calif., Oct. 1977.</ref><ref>M.E. Hellman and J.M. Reyneri, ''Fast computation of discrete logarithms in GF''(q), Advances in Cryptology – -Proceedings of Crypto, 1983</ref> [[Leonard Adleman|Adleman]] optimized the algorithm and presented it in the present form.<ref>L. Adleman, ''A subexponential algorithm for the discrete logarithm problem with applications to cryptography'', In 20th Annual Symposium on Foundations of Computer Science, 1979</ref>
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