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Secure simultaneous bit extraction from Koblitz curves

  • Xinxin Fan
  • Guang Gong
  • Berry Schoenmakers
  • Francesco Sica
  • Andrey Sidorenko
Article
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Abstract

Secure pseudo-random number generators (PRNGs) have a lot of important applications in cryptography. In this paper, we analyze a new PRNG related to the elliptic curve power generator. The new PRNG has many desirable randomness properties such as long period, uniform distribution, etc. In particular, the proposed PRNG is provably secure under the l-strong Diffie–Hellman assumptions. An important feature of our PRNG is that many bits can be simultaneously output without significantly affecting its security. For instance, at 150-bit security, more than 100 bits can be output at each iteration, with a statistical distance from a uniform sequence less than \(1/2^{150}\). Our experimental results show that the new PRNG provides a secure and flexible solution for high security applications. Hence, our work is another step towards the construction of provably secure PRNGs in practice.

Keywords

Cryptography Elliptic curves Pseudo-random Number generator 

Mathematics Subject Classification

11T23 11K45 94A60 
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Notes

Acknowledgements

We thank the referees, whose constructive comments greatly improved the presentation of our work.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IoTeXMenlo ParkUSA
  2. 2.Department of Electrical and Computer EngineeringUniversity of WaterlooWaterlooCanada
  3. 3.Department of Mathematics and Computer ScienceTechnical University EindhovenEindhovenThe Netherlands
  4. 4.School of Science and TechnologyNazarbayev UniversityAstanaKazakhstan
  5. 5.BrightsightDelftThe Netherlands

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