CS 276 – Cryptography March 8 , 2016 Lecture 15 : MPC in the head

Zero knowledge proofs are one of the most used fundamental building blocks in Cryptography. Recall that zero knowledge proofs allow a prover to prove to a verifier about the veracity of a statement without revealing anything beyond the assertion. Zero knowledge proofs have notably found several applications in the area of secure multiparty computation. Secure multiparty computation allows a set of n mutually distrusting parties to compute a joint function of their private inputs. The security guarantee is that any algorithm that corrupts even all but one of the n parties cannot learn anything about the input of the uncorrupted parties beyond what it can learn from the function output. The security of MPC comes in different flavors depending on “how” the parties are corrupted. If the corruption algorithm follows the protocol description but may try to learn arbitrary information from the protocol transcripts then we call it as the semi-honest setting. On the other hand, if the corruption algorithm can deviate arbitrarily from the protocol description then we term it as malicious setting. Notice that malicious MPC even for the case of two parties directly implies Zero Knowledge protocol. 1 In 2007, Ishai, Kushilevitz, Ostrovsky and Sahai proved a surprising result that even semi-honest MPC is sufficient to obtain Zero Knowledge proofs. Additionally the Zero Knowledge protocol obtained as a result of their transformation has some “nice” properties like low communication complexity.