Zero-Knowledge Proofs on Secret-Shared Data via Fully Linear PCPs

BLAZE: Blazing Fast Privacy-Preserving Machine Learning

“…Layer-I: Secondary Building Blocks for PPML -Multiplication: We propose a new and efficient multiplication protocol for the 3 server setting that can tolerate at most one malicious corruption. Our construction invokes the multiplication protocol of [17] (which uses distributed Zero Knowledge) in the preprocessing phase to facilitate an efficient online phase. Concretely, our protocol requires an amortized communication of 3 ring elements in both the preprocessing and online phases.…”

“…This construct serves as the primary building block for our dot product protocol. While the multiplication protocol of [17] performs better than ours with a communication complexity of 3 ring elements overall yet in an amortized sense, we choose our construct over it mainly due to the huge benefits it brings for the case of dot product protocol. The dot product for n-length vectors can be viewed as n multiplications.…”

“…The dot product for n-length vectors can be viewed as n multiplications. Using [17] for the same will result in a communication of 3n (amortized) ring elements in the online phase. For the communication cost to get amortized, the protocol of [17] requires a large number of multiplications to be performed together, which cannot be guaranteed for several instances such as inference phases of Linear Regression and Logistic Regression.…”

“…Using [17] for the same will result in a communication of 3n (amortized) ring elements in the online phase. For the communication cost to get amortized, the protocol of [17] requires a large number of multiplications to be performed together, which cannot be guaranteed for several instances such as inference phases of Linear Regression and Logistic Regression. Furthermore, their protocol makes use of expensive public-key cryptography, which is undesirable in settings similar to ours, where practical efficiency is of utmost importance in the online phase.…”

“…It allows n mutually distrusting parties to perform computations together on their private inputs, so that an adversary controlling at most t parties, can not learn any information beyond what is already known and permissible by the computation. MPC for a small number of parties in the honest majority setting, specifically the setting of 3 parties with one corruption, has become popular over the last few years due to its spectacular performance [7]- [17], leveraging the presence of single corruption. Applications such as financial data analysis [18], email spam filtering [19], distributed credential encryption [12], privacy-preserving statistical studies [20] and popular MPC frameworks such as Sharemind [21], VIFF [22] involve 3 parties.…”