Proof of Plaintext Knowledge for the Ajtai-Dwork Cryptosystem

  • Shafi Goldwasser
  • Dmitriy Kharchenko
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3378)

Abstract

Ajtai and Dwork proposed a public-key encryption scheme in 1996 which they proved secure under the assumption that the unique shortest vector problem is hard in the worst case. This cryptosystem and its extension by Regev are the only one known for which security can be proved under a worst case assumption, and as such present a particularly interesting case to study.

In this paper, we show statistical zero-knowledge protocols for statements of the form “plaintext m corresponds to ciphertext c” and “ciphertext c and c’ decrypt to the same value” for the Ajtai-Dwork cryptosystem. We then show a interactive zero-knowledge proof of plaintext knowledge (PPK) for the Ajtai-Dwork cryptosystem, based directly on the security of the cryptosystem rather than resorting to general interactive zero-knowledge constructions. The witness for these proofs is the randomness used in the encryption.

Keywords

Lattices Verifiable Encryption Ajtai-Dwork Cryptosystem Worst Case Complexity Assumption Proof of Plaintext Knowledge 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Shafi Goldwasser
    • 1
    • 2
  • Dmitriy Kharchenko
    • 2
  1. 1.CSAILMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of Computer Science and Applied MathematicsWeizmann Institute of ScienceRehovotIsrael

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