Efficient Three-party Boolean-to-Arithmetic Share Conversion

The advantage of mixed-protocol multi-party secure computation frameworks lies in their ability to utilize different sharing types optimally for diverse tasks. A key module in these frameworks are Boolean-to-arithmetic secret sharing conversion protocols, which transfer a secret value from Boolean secret sharing to arithmetic secret sharing. This conversion process can either take in the Boolean secret sharing of a bit or a secret binary string. In this work, we suggest the application of an innovative correlated random tuple for this task in the semi-honest three-party (3PC) setting. This tuple provides the basis for building Boolean-to-arithmetic share conversion protocols. Specifically, we propose two such protocols in the semi-honest 3PC setting, the first protocol takes as input the Boolean secret sharing of a bit, and the second protocol takes as input the Boolean secret sharing of a secret binary string. When it comes to concrete efficiency, the first protocol shows superior performance compared to the existing state-of-the-art in ABY3 (CCS '18). It achieves this by reducing the total required communication from $2\ell$ bits per party to $4\ell/3+1$ bits (including $4\ell/3$ bits in the setup phase, and $1$ bit in the online phase) per party, while maintaining a single round of optimized communication. On the other hand, the second protocol involves two rounds of online communication and its communication cost is comparable to that of ABY2.0 (USENIX'21) that relies on correlated oblivious transfer.