Fast probabilistic RAM simulation of single tape turing machine computations
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Fast simulation of Turing machines by random access machines
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Minimum disclosure proofs of knowledge
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STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Universal one-way hash functions and their cryptographic applications
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One-way functions are necessary and sufficient for secure signatures
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Checking computations in polylogarithmic time
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An O(T log T) reduction from RAM computations to satisfiability
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Checking the correctness of memories
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A note on efficient zero-knowledge proofs and arguments (extended abstract)
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Optimal on-line simulations of tree machines by random access machines
SIAM Journal on Computing
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On quasilinear-time complexity theory
STACS '94 Selected papers of the eleventh symposium on Theoretical aspects of computer science
Software protection and simulation on oblivious RAMs
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Finite fields
On the complexity of interactive proofs with bounded communication
Information Processing Letters
Journal of the ACM (JACM)
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Satisfiability Is Quasilinear Complete in NQL
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CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
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Fast probabilistic algorithms for hamiltonian circuits and matchings
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Speedups of deterministic machines by synchronous parallel machines
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
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Robust pcps of proximity, shorter pcps and applications to coding
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The KR-Benes Network: A Control-Optimal Rearrangeable Permutation Network
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CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
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Locally testable codes and PCPs of almost-linear length
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IEEE Transactions on Computers
Delegating computation: interactive proofs for muggles
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Short PCPs with Polylog Query Complexity
SIAM Journal on Computing
Succinct NP Proofs from an Extractability Assumption
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
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Improved delegation of computation using fully homomorphic encryption
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CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
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Succinct arguments for NP are proof systems that allow a weak verifier to retroactively check computation done by a powerful prover. Constructions of such protocols prove membership in languages consisting of very large yet succinctly-represented constraint satisfaction problems that, alas, are unnatural in the sense that the problems that arise in practice are not in such form. For general computation tasks, the most natural representation is typically as random-access machine (RAM) algorithms, because such a representation can be obtained very efficiently by applying a compiler to code written in a high-level programming language. Thus, understanding the efficiency of reductions from RAM computations to other NP-complete problem representations for which succinct arguments (or proofs) are known is a prerequisite to a more complete understanding of the applicability of these arguments. Existing succinct argument constructions rely either on circuit satisfiability or (in PCP-based constructions) on algebraic constraint satisfaction problems. In this paper, we present new and more efficient reductions from RAM (and parallel RAM) computations to both problems that (a) preserve succinctness (i.e., do not "unroll" the computation of a machine), (b) preserve zero-knowledge and proof-of-knowledge properties, and (c) enjoy fast and highly-parallelizable algorithms for transforming a witness for the RAM computation into a witness for the corresponding problem. These additional properties are typically not considered in "classical" complexity theory but are often required or very desirable in the application of succinct arguments. Fulfilling all these efficiency requirements poses significant technical challenges, and we develop a set of tools (both unconditional and leveraging computational assumptions) for generically and efficiently structuring and arithmetizing RAM computations for use in succinct arguments. More generally, our results can be applied to proof systems for NP relying on the aforementioned problem representations; these include various zero-knowledge proof constructions.