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Section: New Results

Efficient Privacy-Preserving Scalar Product

We have designed, implemented and evaluated two variants of new privacy-preserving scalar product protocols. The first variant is based on an original idea of Ioannidis et al.  [8] and was refined by Amirbekyan et al.  [6] . Our first design improves on this by supporting signed values. A second design uses discrete logarithms over Elliptic curves instead of a homomorphic cipher, resulting in a substantially more efficient computation as long as the final result is numerically small.

In both protocols, Alice learns the scalar product $\sum a_i{b}_i$ of her private vector $\overrightarrow{a}$ with Bob's private vector $\overrightarrow{b}$. The protocol is privacy-preserving in that Alice cannot discern details about $\overrightarrow{b}$ other than what she can learn from $\overrightarrow{a}$ and the scalar product $\sum a_i{b}_i$, and Bob does not learn anything.

Table 1 summarizes our experimental results.