The Past, Evolving Present, and Future of the Discrete Logarithm

@inproceedings{Joux2014ThePE,
  title={The Past, Evolving Present, and Future of the Discrete Logarithm},
  author={Antoine Joux and Andrew M. Odlyzko and C{\'e}cile Pierrot},
  booktitle={Open Problems in Mathematics and Computational Science},
  year={2014}
}
The first practical public key cryptosystem ever published, the Diffie–Hellman key exchange algorithm, relies for its security on the assumption that discrete logarithms are hard to compute. This intractability hypothesis is also the foundation for the security of a large variety of other public key systems and protocols. 
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