Joint Encryption and Message-Efficient Secure Computation

  • Matthew Franklin
  • Stuart Haber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 773)


This paper connects two areas of recent cryptographic research: secure distributed computation, and group-oriented cryptography. We construct a probabilistic public-key encryption scheme with the following properties:
  1. It is easy to encrypt using the public keys of any subset of parties, such that it is hard to decrypt without the cooperation of every party in the subset.

  2. It is easy for any private key holder to give a “witness” of its contribution to the decryption (e.g., for parallel decryption).

  3. It is “blindable”: From an encrypted bit it is easy for anyone to compute a uniformly random encryption of the same bit.

  4. It is “xor-homomorphic”: Prom two encrypted bits it is easy for anyone to compute an encryption of their xor.

  5. It is “compact”: The size of an encryption does not depend on the number of participants.


Using this joint encryption scheme as a tool, we show how to reduce the message complexity of secure computation versus a passive adversary (gossiping faults).


Encryption Scheme Quadratic Residue Message Complexity Boolean Circuit Quadratic Character 
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.


  1. 1.
    D. Beaver, “Secure multiparty protocols and zero-knowledge proof systems tolerating a faulty minority,” J. Cryptology (1991) 4: 75–122.CrossRefzbMATHGoogle Scholar
  2. 2.
    D. Chaum, I. Damgård, and J. van de Graaf, “Multiparty computations ensuring privacy of each party’s input and correctness of the result,” Crypto 1987, 87–119.Google Scholar
  3. 3.
    Y. Desmedt, “Society and group oriented cryptography: A new concept,” Crypto 1987, 120–127.Google Scholar
  4. 4.
    Y. Desmedt and Y. Frankel, “Threshold cryptosystems,” Crypto 1989, 307–315.Google Scholar
  5. 5.
    W. Diffie and M. Hellman, “New directions in cryptography,” IEEE Transactions on Information Theory, 22(6):644–654, 1976.CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    T. El-Gamal, “A public key cryptosystem and a signature scheme based on discrete logarithms,” IEEE Transactions on Information Theory, 31:469–472, 1985.CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Z. Galil, S. Haber, and M. Yung, “Cryptographic computation: secure fault-tolerant protocols and the public-key model,” Crypto 1987, 135–155.Google Scholar
  8. 8.
    O. Goldreich, S. Micali, and A. Wigderson, “How to play any mental game,” STOC 1987, 218–229.Google Scholar
  9. 9.
    O. Goldreich and R. Vainish, “How to solve any protocol problem — an efficiency improvement,” Crypto 1987, 73–86.Google Scholar
  10. 10.
    S. Goldwasser and S. Micali, “Probabilistic encryption,” JCSS, 28(2):270:299, 1984.zbMATHMathSciNetGoogle Scholar
  11. 11.
    K. McCurley, “A key distribution system equivalent to factoring,” J. Crypt., l(2):95–105, 1988.CrossRefMathSciNetGoogle Scholar
  12. 12.
    S. Micali, “Fair public-key cryptosystems,” Crypto 1992, 3.11–3.24 (pre-proceedings abstracts).Google Scholar
  13. 13.
    S. Micali and P. Rogaway, “Secure Computation,” Crypto 1991, 392–404.Google Scholar
  14. 14.
    A. Yao, “How to generate and exchange secrets,” FOCS 1986, 162–167.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Matthew Franklin
    • 1
  • Stuart Haber
    • 2
  1. 1.Columbia UniversityNew York
  2. 2.BellcoreMorristown

Personalised recommendations