CT-ISG: New Directions in Cryptographic Proof Systems

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Cryptographic proof systems have played an instrumental role incryptography. The applications of cryptographic proof systems to an widearray of problems such as electronic voting, database security, secureelectronic commerce, identity management, computing on secret data,trusted computing, and networking are well know. Significant efficiencybarriers remain to the widespread use of general cryptographic proofsystems. We propose an ambitious focused research plan to overcome thesebarriers, by developing a new methodology based on elliptic-curve groupsto dramatically increase the efficiency of cryptographic proof systems.Our research plan has two main technical thrusts:(1) We propose to introduce a new technical framework for constructingnon-interactive cryptographic proof systems (such as zero-knowledgeproofs), based on a direct commit-and-prove technique. Our frameworkpromises to greatly reduce proof sizes for cryptographic proofs. In themost general setting, where we are given a boolean circuit C and wish toprove that there exists some input x such that C(x) = 1, we seek proofsthat contain only O(|C|) group elements, where |C| denotes the size of thecircuit. (2) The very act of interpreting the statement to be proven as a booleancircuit itself often introduces a substantial overhead. We observe thatthere has been considerable recent development of cryptographic schemesbased on bilinear groups. We propose to develop a set of techniques thatcan be used to directly prove a variety of interesting statements aboutessentially any cryptographic scheme based on bilinear groups.