Paper 2005/066
Unconditionally Secure Constant Round MultiParty Computation for Equality, Comparison, Bits and Exponentiation
Eike Kiltz
Abstract
In this paper we are interested in efficient and secure constant round multiparty protocols which provide unconditional security against so called honestbutcurious adversaries. In particular, we design a novel constant round protocol that converts from shares over Z_q to shares over the integers working for all shared inputs from Z_q. Furthermore, we present a constant round protocol to securely evaluate a shared input on a public polynomial whose running time is linear in the degree of the polynomial. The proposed solution makes use of Chebyshev Polynomials. We show that the latter two protocols can be used to design efficient constant round protocols for the following natural problems: (i) Equality: Computing shares of the bit indicating if a shared input value equals zero or not. This provides the missing building blocks for many constant round linear algebra protocols from the work of Cramer and Damgaard [CrDa01]. (ii) Comparison: Computing shares of a bit indicating which of two shared inputs is greater. (iii) Bits: Computing shares of the binary representation of a shared input value. (iv) Exponentiation: Computing shares of x^a mod q given shares of x, a and q. Prior to this paper, for all the above mentioned problems, there were in general no efficient constant round protocols known providing unconditional security.
Note: A bug in the conversion protocol has been fixed in this revision.
Metadata
 Available format(s)
 PDF PS
 Category
 Cryptographic protocols
 Publication info
 Published elsewhere. Unknown where it was published
 Keywords
 multiparty computationunconditional securitysecret sharing
 Contact author(s)
 ekiltz @ cs ucsd edu
 History
 20050520: revised
 20050301: received
 See all versions
 Short URL
 https://ia.cr/2005/066
 License

CC BY
BibTeX
@misc{cryptoeprint:2005/066, author = {Eike Kiltz}, title = {Unconditionally Secure Constant Round MultiParty Computation for Equality, Comparison, Bits and Exponentiation}, howpublished = {Cryptology {ePrint} Archive, Paper 2005/066}, year = {2005}, url = {https://eprint.iacr.org/2005/066} }