Advertisement

Low-randomness constant-round private XOR computations

  • Carlo Blundo
  • Clemente GaldiEmail author
  • Giuseppe Persiano
Regular Contribution

Abstract

In this paper we study the randomness complexity needed to distributively perform k XOR computations in a t-private way using constant-round protocols in the case in which the players are honest but curious.

We show that the existence of a particular family of subsets allows the recycling of random bits for constant-round private protocols. More precisely, we show that after a 1-round initialization phase during which random bits are distributed among n players, it is possible to perform each of the k XOR computations using two rounds of communication.

For \(t\leq c\sqrt{n/\log n}\), for any c < 1/2, we design a protocol that uses O(kt 2log n) random bits.

Keywords

Multiparty computation Randomness 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bar-Ilan, J., Beaver, D. Non-cryptographic fault-tolerant computing in a constant number of round of interaction. In: Proceedings of 8th ACM Symposium on Principles of Distributed Computing, pp. 36–44 (1989)Google Scholar
  2. 2.
    Beaver, D., Feigenbaum, J., Kilian, J., Rogaway, P. Security with low communication overhead. In: Advances in Cryptology – CRYPTO 90, pp. 62–76 (1990)Google Scholar
  3. 3.
    Beaver, D., Micali, S., Rogaway, P. The round complexity of secure protocols. In: Proceedings of 22nd Symposium on Theory of Computing, pp. 503–513 (1990)Google Scholar
  4. 4.
    Ben-Or, M., Goldwasser, S., Wigderson, A. Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proceedings of 20th Symposium on Theory of Computing, pp. 1–10 (1988)Google Scholar
  5. 5.
    Benaloh J. (1986). Secret sharing homomorphism: Keeping shares of a secret secret. In: Odlyzko A. (eds). Advances in Cryptography – Crypto 86. Lecture Notes in Computer Science, vol. 263, Springer, Berlin Heidelberg New York, pp. 251–260Google Scholar
  6. 6.
    Blundo, C., Galdi, C., Persiano, P. Randomness recycling in constant round private computations. In: Jayanti, P. (ed.) Proceedings of 13th International Symposium on Distributed Computing (DISC 99), vol. 1693 of LNCS, pp. 138–150 (1999)Google Scholar
  7. 7.
    Blundo C., Santis A.D., Persiano G., Vaccaro U. (1999) Randomness complexity of private multiparty protocols. Comput. Complex. 8(2): 145–168CrossRefGoogle Scholar
  8. 8.
    Canetti R., Kushilevitz E., Ostrovsky R., Rosén A. (2000) Randomness versus fault-tolerance. J. Cryptol. 13(1): 107–142CrossRefGoogle Scholar
  9. 9.
    Chaum, D., Crepeau, C., Damgärd, I. Multiparty unconditionally secure protocols. In: Proceedings of 20th Symposium on Theory of Computing, pp. 11–19 (1988)Google Scholar
  10. 10.
    Chor B., Kushilevitz E. (1991) A communication-privacy tradeoff for modular addition. Inf. Process. Lett. 45, 205–210CrossRefMathSciNetGoogle Scholar
  11. 11.
    Chor B., Kushilevitz E. (1991) A zero-one law for boolean privacy. SIAM J. Discrete Mat. 4(1): 36–46CrossRefMathSciNetGoogle Scholar
  12. 12.
    Du D., Hwang F. (1993) Combinatorial Groups Testing and its Applications. World Scientific, SingaporeGoogle Scholar
  13. 13.
    Erdös P., Frankl P., Füredi Z. (1985) Families of finite sets in which no set is covered by the union of r others. Isr. J. Math. 51: 79–89Google Scholar
  14. 14.
    Kushilevitz E., Mansour Y. (1997) Randomness in private computations. SIAM J. Discrete Math. 10(4): 647–651CrossRefMathSciNetGoogle Scholar
  15. 15.
    Kushilevitz, E., Ostrovsky, R., Rosèn, A. Characterizing linear size circuit in terms of privacy. In: Proceedings of 28th ACM Symposium on Theory of Computing (1996)Google Scholar
  16. 16.
    Kushilevitz, E., Ostrovsky, R., Rosèn, A.: Amortizing randomness in private multiparty computations. In: Proceedings of 17th ACM Symposium on Principles of Distributed Computing (1998)Google Scholar
  17. 17.
    Kushilevitz E., Rosèn A. (1998) A randomness-round tradeoff in private computation. SIAM J. Discerete Math. 11(1): 61–80CrossRefGoogle Scholar
  18. 18.
    Lang, S. Linear Algebra. Addison-Wesley, ReadingGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Carlo Blundo
    • 1
  • Clemente Galdi
    • 2
    Email author
  • Giuseppe Persiano
    • 1
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversità di SalernoFiscianoItaly
  2. 2.Dipartimento di Scienze FisicheUniversità di Napoli “Federico II”NapoliItaly

Personalised recommendations