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The Insecurity of Nyberg-Rueppel and Other DSA-Like Signature Schemes with Partially Known Nonces

  • Edwin El Mahassni
  • Phong Q. Nguyen
  • Igor E. Shparlinski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2146)

Abstract

It has recently been proved by Nguyen and Shparlinski that the Digital Signature Algorithm (DSA) is insecure when a few consecutive bits of the random nonces k are known for a reasonably small number of DSA signatures. This result confirmed the efficiency of some heuristic lattice attacks designed and numerically verified by Howgrave-Graham and Smart. Here, we extend the attack to the Nyberg-Rueppel variants of DSA. We use a connection with the hidden number problem introduced by Boneh and Venkatesan and new bounds of exponential sums which might be of independent interest.

Keywords

DSA Closest Vector Problem Hidden Number Problem Exponential Sums 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Edwin El Mahassni
    • 1
  • Phong Q. Nguyen
    • 2
  • Igor E. Shparlinski
    • 3
  1. 1.Department of ComputingMacquarie UniversityAustralia
  2. 2.Département d’InformatiqueÉcole Normale SupérieureParisFrance
  3. 3.Department of ComputingMacquarie UniversityAustralia

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