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Cryptanalysis of the Ajtai-Dwork cryptosystem

  • Phong Nguyen
  • Jacques Stern
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1462)

Abstract

Recently, Ajtai discovered a fascinating connection between the worst-case complexity and the average-case complexity of some wellknown lattice problems. Later, Ajtai and Dwork proposed a cryptosystem inspired by Ajtai's work, provably secure if a particular lattice problem is difficult in the worst-case. We present a heuristic attack (to recover the private key) against this celebrated cryptosystem. Experiments with this attack suggest that in order to be secure, implementations of the Ajtai-Dwork cryptosystem would require very large keys, making it impractical in a real-life environment. We also adopt a theoretical point of view: we show that there is a converse to the Ajtai-Dwork security result, by reducing the question of distinguishing encryptions of one from encryptions of zero to approximating some lattice problems. In particular, this settles the open question regarding the NP-hardness of the Ajtai-Dwork cryptosystem: from a recent result of Goldreich and Goldwasser, our result shows that breaking the Ajtai-Dwork cryptosystem is not NP-hard, assuming the polynomial-time hierarchy does not collapse.

Keywords

Short Vector Multinomial Formula Close Vector Problem Close Vector Problem Lattice Reduction Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Phong Nguyen
    • 1
  • Jacques Stern
    • 1
  1. 1.Laboratoire d'Informatiqueécole Normale SupérieureParis Cedex 05

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