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City Pairing / / Company Diffie-Hellman Key Exchange Let us / Let us / / / Event FDA Phase / / Facility University of Minnesota / / IndustryTerm generic / secure protocols / point counting algorithms / presents concrete algorithms / quantum algorithm / designed key exchange protocol / typical solution / candidate replacement systems / generic group algorithms / generic algorithm / classical systems / past communications / generic algorithms / agreement protocol / proper key management / classical protocols / faster algorithm / cryptographic protocols / public key systems / subexponential algorithms / earlier communications / binary search / important applications / cycle finding algorithms / identification protocol / elliptic curve systems / fine solution / collision search / computing / finite / arbitrary groups / / Organization School of Mathematics / UPMC Univ Paris / University of Minnesota / Minneapolis / / Person Andrew Odlyzko / John M. Pollard / Antoine Joux / Cécile Pierrot / Now Alice / Charlie / Bob / Alice / Step Let / / Position hb / model / / Product Franklin / BD94 / Jou04 / Sch89 / / Technology pairing-based protocols / quantum algorithm / key exchange algorithm / Pollard Rho algorithms / Hellman algorithm / cycle finding algorithms / key exchange protocol / key exchange protocols / Paillier encryption / DES algorithm / generic algorithm / BurmesterDesmedt protocol / private key / NO. An algorithm / secret key / one-round protocol / using point counting algorithms / encryption / The Pohlig-Hellman algorithm / cryptography / threeparty one-round key agreement protocol / public key / Shanks algorithm / identification protocol / correctly designed key exchange protocol / DLP / 4 presents concrete algorithms / Rho algorithm / Pollard Rho algorithm / /
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The Past, evolving Present and Future of Discrete Logarithm Antoine Joux, Andrew Odlyzko and Cécile Pierrot Abstract The first practical public key cryptosystem ever published, the Diffie-Hellman key exchange algorithm,