Constructions for Conditional Oblivious/converge Transfer/cast Constructions for Conditional Oblivious/converge Transfer/cast

In this paper, we introduce a new notion of conditional converge cast (CCC), such that we append the conditional property to converge cast. Additionally, we generalize the three primitives with conditional property, conditional oblivious transfer (COT), conditional oblivious cast (COC), and CCC. CCC is a three-party protocol which involves two senders S0 and S1 and a receiver R. S0 owns a secret x and a message m0, and S1 y and m1. In a CCC protocol for the predicate Q (Q-CCC), S0 and S1 send their messages to R in a masked form. R obtains the message depending on the value of Q(x, y), i.e. R obtains m0 if Q(x, y) = 0 and m1 otherwise. Besides, the secrets x and y cannot be revealed to R or the other sender. We propose a CCC protocol for “equality” predicate with an additively homomorphic encryption scheme. Additionally, we extend 1-out-of-2 COT/COC/CCC to 1-out-of-n COT/COC/CCC. In 1-out-of-2 protocols, a sender or senders send two messages to a receiver or receivers. In 1-outof-n protocols, a sender or senders send n messages, where n = 2 for some l. We provide the consecutive definitions and the concrete protocols for 1-out-of-n COT/COC/CCC protocols. We prove that our protocols are secure under the security of 1-out-of-2 protocols.