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A Leakage-Resilient Zero Knowledge Proof for Lattice Problem

  • Yang Liu
  • Hongda Li
  • Qihua Niu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7672)

Abstract

Leakage-resilient cryptographic protocols have recently been evolving intensively, studying the question of designing protocol that maintain security even in the presence of side-channel attacks. Under leakage assumption(the verifier uses side-channel attacks to obtain some information about the secret state of the prover), the known zero knowledge protocol may not preserve zero knowledge any more. Garg et.al. first studied leakage-resilient zero knowledge and presented an excellent construction for NP. Unfortunately, the definition is not suitable for honest verifier leakage-resilient zero knowledge. In this paper, we give a new definition of leakage-resilient zero knowledge and construct a leakage-resilient zero knowledge proof for approximate version of the closest vector problem(\(\textsc{G}_{\textsc{AP}}\textsc{CVP}_\gamma\)). We also give a definition of leakage-resilient bit commitment scheme.

Keywords

leakage-resilient zero knowledge proof lattice commitment 

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References

  1. [Ajt11]
    Ajtai, M.: Secure computation with information leaking to an adversary. In: Proceedings of the 43rd ACM Symposium on Theory of Computing, STOC 2011, San Jose, CA, USA, June 6-8, pp. 715–724. ACM (2011)Google Scholar
  2. [CGGM00]
    Canetti, R., Goldreich, O., Goldwasser, S., Micali, S.: Resettable zero knowledge. In: Proc. 32nd STOC, pp. 235–244 (2000)Google Scholar
  3. [DHP11]
    Damgård, I., Hazay, C., Patra, A.: Leakage Resilient Secure Two-Party Computation. IACR Cryptology ePrint Archive 2011: 256 (2011)Google Scholar
  4. [DNS98]
    Dwork, C., Naor, M., Sahai, A.: Concurrent zero knowledge. In: Proc. 30th STOC, pp. 409–418 (1998)Google Scholar
  5. [GGH97]
    Goldreich, O., Goldwasser, S., Halevi, S.: Public-Key Cryptosystems from Lattice Reduction Problems. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 112–131. Springer, Heidelberg (1997)Google Scholar
  6. [GG00]
    Goldreich, O., Goldwasser, S.: On the limits of nonapproximability of lattice problems. J. Comput. System Sci. 60, 540–563 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. [GJS11]
    Garg, S., Jain, A., Sahai, A.: Leakage-Resilient Zero Knowledge. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 297–315. Springer, Heidelberg (2011)Google Scholar
  8. [GK96]
    Goldreich, O., Kahan, A.: How to construct constant-round zero-knowledge proof systems for NP. Journal of Cryptology 9(3), 167–189 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  9. [GMR89]
    Goldwasser, S., Micali, S., Rachoff, C.: The knowledge complexity of interactive proof systems. Journal on Computing 18(1), 186–208 (1989)MathSciNetzbMATHGoogle Scholar
  10. [Mic01]
    Micciancio, D.: Improving Lattice Based Cryptosystems Using the Hermite Normal Form. In: Silverman, J.H. (ed.) CaLC 2001. LNCS, vol. 2146, pp. 126–145. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. [MV03]
    Micciancio, D., Vadhan, S.P.: Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 282–298. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. [OST06]
    Osvik, D.A., Shamir, A., Tromer, E.: Cache Attacks and Countermeasures: The Case of AES. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 1–20. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. [Pan12]
    Pandey, O.: Achieving Constant Round Leakage-Resilient Zero-Knowledge. IACR Cryptology ePrint Archive 2012: 362 (2012)Google Scholar
  14. [PRS02]
    Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent zero knowledge with logarithmic round-complexity. In: FOCS (2002)Google Scholar
  15. [Vad99]
    Vadhan, S.P.: A Study of Statistical Zero-Knowledge Proofs. Massachusetts Institute of Technology (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yang Liu
    • 1
  • Hongda Li
    • 1
  • Qihua Niu
    • 1
  1. 1.State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of SciencesBeijingChina

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