Secure Set Membership Using 3Sat
A wide variety of powerful cryptographic tools have been built using RSA, Diffie-Hellman, and other similar assumptions as their basis. Computational security has been achieved relative to complexity assumptions about the computational difficulty of a variety of number theoretic problems. However, these problems are closely related, and it is likely that if any one of them turns out to be efficiently solvable with new mathematical advances or new kinds of computational devices, then similar techniques could be applicable to all of them. To provide greater diversity of security assumptions so that a break of one of them is less likely to yield a break of many or all of them, it is important to expand the body of computational problems on which security systems are based. Specifically, we suggest the use of hardness assumptions based on the complexity of logic problems, and in particular, we consider the well known Boolean 3Sat problem.
In this paper, we consider the use of the 3Sat problem to provide a cryptographic primitive, secure set membership. Secure set membership is a general problem for participants holding set elements to generate a representation of their set that can then be used to prove knowledge of set elements to others. Set membership protocols can be used, for example, for authentication problems such as digital credentials and some signature problems such as timestamping.
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- 1.Acquisiti, A.: Anonymous credentials through acid mixing (2003) (upublished manuscript)Google Scholar
- 2.Alekhnovich, M., Ben-Sasson, E.: Linear upper bounds for random walk on small density random 3-CNFs. In: Proceedings of the 44th Annual IEEE Symposium on the Foundations of Computer Science (2003)Google Scholar
- 3.Baric, N., Pfitzmann, B.: Collision-free accumulators and fail-stop signature schemes without trees. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 480–494. Springer, Heidelberg (1997)Google Scholar
- 4.Benaloh, J.: Verifiable Secret-Ballot Elections. PhD thesis, Yale University Department of Computer Science (September 1987)Google Scholar
- 5.Benaloh, J., de Mare, M.: Efficient broadcast time-stamping. Technical Report TR-MCS-91-1, Clarkson University Department of Mathematics and Computer Science (1991)Google Scholar
- 6.Benaloh, J., de Mare, M.: One-way accumulators: A decentralized approach to digital signatures. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 274–285. Springer, Heidelberg (1994)Google Scholar
- 8.Brassard, G., Crepeau, C.: Zero-knowledge simulation of boolean circuits. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 223–233. Springer, Heidelberg (1987)Google Scholar
- 11.de Mare, M.: An analysis of certain cryptosystems and related mathematics. Master’s thesis, State University of New York Institute of Technology (December 2004)Google Scholar
- 13.Esponda, F.: Negative Representations of Information. PhD thesis, University of New Mexico (2005)Google Scholar
- 15.Esponda, F., Forrest, S., Helman, P.: Enhancing privacy through negative representations of data. Technical report, University of New Mexico (2004)Google Scholar
- 16.Esponda, F., Forrest, S., Helman, P.: Information hiding through negative representations of data. Technical report, University of New Mexico (2004)Google Scholar
- 17.Goldreich, O., Micali, S., Wigderson, A.: How to prove all NP statements in zero-knowledge and a methodology of cryptographic protocol design. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 171–185. Springer, Heidelberg (1987)Google Scholar
- 23.Merkle, R.C.: Secrecy, authentication, and public key systems. UMI Research Press (1982)Google Scholar
- 24.Merkle, R.C.: A digital signature based on a conventional encryption function. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 369–378. Springer, Heidelberg (1988)Google Scholar
- 25.Odlyzko, A.M.: The rise and fall of the knapsack cryptosystems. In: PSAM: Proceedings of the 42nd Symposium in Applied Mathematics, pp. 75–88 (1990)Google Scholar