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Efficient Public Key Encryption Based on Ideal Lattices

(Extended Abstract)
  • Damien Stehlé
  • Ron Steinfeld
  • Keisuke Tanaka
  • Keita Xagawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5912)

Abstract

We describe public key encryption schemes with security provably based on the worst case hardness of the approximate Shortest Vector Problem in some structured lattices, called ideal lattices. Under the assumption that the latter is exponentially hard to solve even with a quantum computer, we achieve CPA-security against subexponential attacks, with (quasi-)optimal asymptotic performance: if n is the security parameter, both keys are of bit-length \({\widetilde{O}}(n)\) and the amortized costs of both encryption and decryption are \({\widetilde{O}}(1)\) per message bit. Our construction adapts the trapdoor one-way function of Gentry et al. (STOC’08), based on the Learning With Errors problem, to structured lattices. Our main technical tools are an adaptation of Ajtai’s trapdoor key generation algorithm (ICALP’99) and a re-interpretation of Regev’s quantum reduction between the Bounded Distance Decoding problem and sampling short lattice vectors.

Keywords

Encryption Scheme Success Probability Quantum Algorithm Ideal Lattice Trapdoor Function 
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 2009

Authors and Affiliations

  • Damien Stehlé
    • 1
    • 2
  • Ron Steinfeld
    • 2
  • Keisuke Tanaka
    • 3
  • Keita Xagawa
    • 3
  1. 1.CNRS/Department of Mathematics and StatisticsUniversity of SydneyAustralia
  2. 2.Centre for Advanced Computing - Algorithms and Cryptography, Department of ComputingMacquarie UniversityAustralia
  3. 3.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyJapan

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