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Classical cryptographic protocols in a quantum world
 of Lecture Notes in Computer Science
, 2011
"... Cryptographic protocols, such as protocols for secure function evaluation, have played a crucial role in the development of modern cryptography. Secure function evaluation (SFE) allows a group of players, each holding a secret input (e.g., a vote) to jointly evaluate some function of their inputs (s ..."
Abstract

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Cryptographic protocols, such as protocols for secure function evaluation, have played a crucial role in the development of modern cryptography. Secure function evaluation (SFE) allows a group of players, each holding a secret input (e.g., a vote) to jointly evaluate some function of their inputs (say, the votes ’ tally) without revealing anything except the function’s value. A special case of this is a zeroknowledge (ZK) proof system, which allows a prover P who knows a short proof of a statement to interactively prove the statement to a computationallybounded verifier V without revealing anything except the statement’s veracity. The very possibility of such protocols is counterintuitive. But a series of seminal results in the 1980’s showed that under mild assumptions (roughly, the existence of secure publickey cryptosystems), SFE protocols exist for any polynomialtime function [22, 10, 3, 29], and ZK proof systems are possible for any language in NP [23]. Research into the design and analysis of these protocols is now a large subfield of cryptography; moreover, it has driven important advances in more traditional areas of cryptography such as the design of encryption, authentication and signature schemes. The extensive theory of these protocols, however, deals almost exclusively with classical attackers. If we accept that quantum information processing is currently the most realistic model of physically feasible computation (we do), then we must ask: what classical protocols remain secure against quantum attackers?