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What is the purpose of ZKPoPK in the SPDZ paper? And will the following can detect the active adversaries in 2 party spdz excluding ZKPoPK step?

  1. Each party sends a commitment on his MAC key ∆_i before starting the offline phase.
  2. Parties select random a_i and b_i and broadcast the encryption on a_i, b_i, ∆_i
  3. These encryptions can be added up and multiplied using FHE to produce encryptions of (a · b, a · ∆, b. ∆, a · b · ∆)
  4. Using the distributed decryption to allow the parties to receive an additive secret sharing of each of those values
  5. Same procedure can be used to authenticate the inputs of each party
  6. Circuit Evaluation
  7. Reveal the output and the mac keys
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