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)


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].


Prime Power Communication Complexity Discrete Logarithm Security Parameter Oblivious Transfer 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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)zbMATHMathSciNetGoogle 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 

Personalised recommendations