Multiparty Computation for Interval, Equality, and Comparison Without Bit-Decomposition Protocol

Damg˚ard et al. [11] showed a novel technique to convert a polynomial sharing of secret a into the sharings of the bits of a in constant rounds, which is called the bit-decomposition protocol. The bitdecomposition protocol is a very powerful tool because it enables bitoriented operations even if shared secrets are given as elements in the field. However, the bit-decomposition protocol is relatively expensive. In this paper, we present a simplified bit-decomposition protocol by analyzing the original protocol. Moreover, we construct more efficient protocols for a comparison, interval test and equality test of shared secrets without relying on the bit-decomposition protocol though it seems essential to such bit-oriented operations. The key idea is that we do computation on secret a with c and r where c = a + r, c is a revealed value, and r is a random bitwise-shared secret. The outputs of these protocols are also shared without being revealed. The realized protocols as well as the ori...

• Type: Conference
• Year: 2007
• Where: PKC
• Authors: Takashi Nishide, Kazuo Ohta
• Keywords: Bit-decomposition Protocol, Cryptography, Original Protocol, PKC 2007, Shared Secrets