Method for faster secure multiparty inner product with SPDZ

A multiparty computation system comprising:

• a first computational party having a first private vector (x={x1, . . . , xN}), where N is a predetermined number;
• a second computational party having a second vector (w={w1, . . . , wN});
• and
• at least one secure communication channel via which the first computational party and the second computational party can securely transmit messages to each other;
• wherein the first computational party and the second computational party are configured to perform a secure multiparty inner product computation based on a speedz protocol (SPDZ protocol) to jointly compute an inner product (d) of the first private vector and the second private vector such that
• x
• 1
• ⁢
• w
• 1
• +
• …
• +
• x
• N
• ⁢
• w
• N
• =
• ∑
• i
• =
• 1
• N
• x
• i
• ⁢
• w
• i
• ,
• without the first computational party learning the second private vector and the second computational party learning the first private vector,
• wherein the secure multiparty inner product computation includes:
• using the SPDZ protocol to securely share the first private vector from the first computational party to the second computational party,
• computing, for i=1, . . . , k, a vector xι={x1, . . . , xk} for the first computational party, where k=N/2 and the value xι=x2i-1x2i, and using the SPDZ protocol to securely share the vector xι with the second computational party,
• using the SPDZ protocol to securely share the second private vector from the second computational party to the first computational party,
• computing, for i=1, . . . , k, a vector wι={w1, . . . , wk} for the second computational party, where the value wι=w2i-1w2i, and using the SPDZ protocol to securely share the vector wι with the first computational party,
• computing, for i=1, . . . , k, shares [w2i-1+x2i] and [w2i+x2i-1] by performing SPDZ protocol Add([x2i-1], [w2i]) and Add([w2i], [x2i-1]), respectively, with the first computational party and the second computational party, the shares [w2i-1+x2i] and [w2i+x2i-1] being shares of (w2i-1+x2i) and (w2i+x2i-1), respectively,
• computing, for i=1, . . . , k, inner product shares [di] by performing SPDZ protocol Mult([w2i-1+x2i], [w2i+x2i-1]) with the first computational party and the second computational party, and
• computing the inner product (d) by performing SPDZ protocol Add([d1], . . . , [dk], −[x1], . . . , −[xk], −[w1], . . . , −[wk]) with the first computational party and the second computational party.