Secure Multi-party Computational Geometry
The general secure multi-party computation problem is when multiple parties (say, Alice and Bob) each have private data (respectively, a and b) and seek to compute some function f(a,b) without revealing to each other anything unintended (i.e., anything other than what can be inferred from knowing f(a,b)). It is well known that, in theory, the general secure multi-party computation problem is solvable using circuit evaluation protocols. While this approach is appealing in its generality, the communication complexity of the resulting protocols depend on the size of the circuit that expresses the functionality to be computed. As Goldreich has recently pointed out , using the solutions derived from these general results to solve specific problems can be impractical; problem-specific solutions should be developed, for efficiency reasons. This paper is a first step in this direction for the area of computational geometry. We give simple solutions to some specific geometric problems, and in doing so we develop some building blocks that we believe will be useful in the solution of other geometric and combinatorial problems as well.
KeywordsOblivious Transfer Boolean Circuit Private Information Retrieval Output Wire Input Wire
Unable to display preview. Download preview PDF.
- 1.Wenliang Du, Mikhail J. Atallah and Florian Kerschbaum. Protocols for secure remote database access with approximate matching. Submitted to a journal, 2001.Google Scholar
- 2.J. Benaloh. Dense probabilistic encryption. In Proceedings of the Workshop on Selected Areas of Cryptography, pages 120–128, Kingston, ON, May 1994.Google Scholar
- 3.C. Cachin. Efficient private bidding and auctions with an oblivious third party. In Proceedings of the 6th ACM conference on Computer and communications security, pages 120–127, Singapore, November 1–4 1999.Google Scholar
- 4.G. Brassard, C. Crépeau and J. Robert. All-or-nothing disclosure of secrets. In Advances in Cryptology-Crypto86, Lecture Notes in Computer Science, volume 234–238, 1987.Google Scholar
- 5.Wenliang Du and Mikhail J. Atallah. Privacy-preserving cooperative scientific computations. In 14th IEEE Computer Security Foundations Workshop, Nova Scotia, Canada, June 11–13 2001.Google Scholar
- 6.O. Goldreich. Secure multi-party computation (working draft). Available from http://www.wisdom.weizmann.ac.il/home/oded/publichtml/foc.html, 1998.
- 8.C. Cachin, S. Micali and M. Stadler. Computationally private information retrieval with polylogarithmic communication. Advances in Cryptology: EUROCRYPT’ 99, Lecture Notes in Computer Science, 1592:402–414, 1999.Google Scholar
- 9.O. Goldreich, S. Micali and A. Wigderson. How to play any mental game. In Proceedings of the 19th annual ACM symposium on Theory of computing, pages 218–229, 1987.Google Scholar
- 10.D. Naccache and J. Stern. A new cryptosystem based on higher residues. In Proceedings of the 5th ACM Conference on Computer and Communications Security, pages 59–66, 1998.Google Scholar
- 11.M. Naor and B. Pinkas. Oblivious transfer and polynomial evaluation (extended abstract). In Proceedings of the 31th ACM Symposium on Theory of Computing, pages 245–254, Atanta, GA, USA, May 1–4 1999.Google Scholar
- 13.T. Okamoto and S. Uchiyama. An efficient public-key cryptosystem. In Advances in Cryptology-EUROCRYPT 98, pages 308–318, 1998.Google Scholar
- 14.P. Paillier. Public-key cryptosystems based on composite degree residue classes. In Advances in Cryptology-EUROCRYPT 99, pages 223–238, 1999.Google Scholar
- 15.A.C. Yao. Protocols for secure computations. In Proceedings of the 23rd Annual IEEE Symposium on Foundations of Computer Science, 1982.Google Scholar
- 16.A.C. Yao. How to generate and exchange secrets. In Proceedings 27th IEEE Symposium on Foundations of Computer Science, pages 162–167, 1986.Google Scholar