Paper 2015/767

Dual EC: A Standardized Back Door

Daniel J. Bernstein, Tanja Lange, and Ruben Niederhagen


Dual EC is an algorithm to compute pseudorandom numbers starting from some random input. Dual EC was standardized by NIST, ANSI, and ISO among other algorithms to generate pseudorandom numbers. For a long time this algorithm was considered suspicious -- the entity designing the algorithm could have easily chosen the parameters in such a way that it can predict all outputs -- and on top of that it is much slower than the alternatives and the numbers it provides are more biased, i.e., not random. The Snowden revelations, and in particular reports on Project Bullrun and the SIGINT Enabling Project, have indicated that Dual EC was part of a systematic effort by NSA to subvert standards. This paper traces the history of Dual EC including some suspicious changes to the standard, explains how the back door works in real-life applications, and explores the standardization and patent ecosystem in which the standardized back door stayed under the radar.

Available format(s)
Publication info
Preprint. MINOR revision.
Random-number generationback doorsNSAANSINISTISORSACerticomundead RNGs.
Contact author(s)
authorcontact-dualec @ box cr yp to
2015-07-31: received
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Creative Commons Attribution


      author = {Daniel J.  Bernstein and Tanja Lange and Ruben Niederhagen},
      title = {Dual {EC}: A Standardized Back Door},
      howpublished = {Cryptology ePrint Archive, Paper 2015/767},
      year = {2015},
      note = {\url{}},
      url = {}
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