Single-Database Private Information Retrieval with Constant Communication Rate

  • Craig Gentry
  • Zulfikar Ramzan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3580)

Abstract

We present a single-database private information retrieval (PIR) scheme with communication complexity \({\mathcal O}(k+d)\), where k ≥ log n is a security parameter that depends on the database size n and d is the bit-length of the retrieved database block. This communication complexity is better asymptotically than previous single-database PIR schemes. The scheme also gives improved performance for practical parameter settings whether the user is retrieving a single bit or very large blocks. For large blocks, our scheme achieves a constant “rate” (e.g., 0.2), even when the user-side communication is very low (e.g., two 1024-bit numbers). Our scheme and security analysis is presented using general groups with hidden smooth subgroups; the scheme can be instantiated using composite moduli, in which case the security of our scheme is based on a simple variant of the “Φ-hiding” assumption by Cachin, Micali and Stadler [2].

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References

  1. 1.
    Beimel, A., Ishai, Y., Kushilevitz, E., Raymond, J.F.: Breaking the O(n 1/(2k − 1) ) Barrier for Information-Theoretic Private Information Retrieval, FOCS 2002 (2002)Google Scholar
  2. 2.
    Cachin, C., Micali, S., Stadler, M.: Computational Private Information Retrieval with Polylogarithmic Communication. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, p. 402. Springer, Heidelberg (1999)Google Scholar
  3. 3.
    Chang, Y.: Single-Database Private Information Retreival with Logarithmic Communication. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) ACISP 2004. LNCS, vol. 3108, pp. 50–61. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Chor, B., Gilboa, N.: Comput. Private Information Retrieval. In: STOC (1997)Google Scholar
  5. 5.
    Chor, B., Kushilevitz, E., Goldreich, O., Sudan, M.: Private Information Retrieval. Journal of the ACM 45 (1998); Earlier version in FOCS 1995Google Scholar
  6. 6.
    Coppersmith, D.: Finding a Small Root of a Bivariate Integer Equation; Factoring with High Bits Known. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 178–189. Springer, Heidelberg (1996)Google Scholar
  7. 7.
    Coppersmith, D.: Finding a Small Root of a Univ. Mod. Equation. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 155–165. Springer, Heidelberg (1996)Google Scholar
  8. 8.
    Damgard, I., Koprowski, M.: Generic Lower Bounds for Root Extraction and Signature Schems in General Groups. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, p. 256. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Kushilevits, E., Ostrovsky, R.: Replication is not needed: single database, computationally private information Retrieval. In: FOCS (1997)Google Scholar
  10. 10.
    Lenstra, A.K., Lenstra Jr., H.W. (eds.): The Development of the Number Field Sieve. Lecture Notes in Mathematics, vol. 1554. Springer, Heidelberg (1995)Google Scholar
  11. 11.
    Lipmaa, H.: An Oblivious Transfer Protocol with Log-Squared Communication. Cryptology ePrint Archive, 2004/063Google Scholar
  12. 12.
    May, A.: A Tool Kit for Finding Small Roots of Bivariate Polynomials over the Integers. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 251–267. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Naor, M., Pinkas, B.: Obl. Transfer and Polynomial Evaluation. In: STOC (1999)Google Scholar
  14. 14.
    Pohlig, S.C., Hellman, M.: An Improved Algorithm for Computing Logarithms Over GF(p) and its Crypt. Significance. IEEE Trans. Inf. Th. IT-24 (1978)Google Scholar
  15. 15.
    Rosser, J.B., Schoenfeld, L.: Sharper Bounds for Chebyshev Functions θ(x) and ψ(x). Math. Comput. 29, 243–269 (1975)MATHMathSciNetGoogle Scholar
  16. 16.
    Stern, J.P.: A New and Efficient All or Nothing Disclosure of Secrets Protocol. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 357–371. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Craig Gentry
    • 1
  • Zulfikar Ramzan
    • 1
  1. 1.DoCoMo Communications Laboratories USA, Inc 

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