NP is as easy as detecting unique solutions
Theoretical Computer Science
Optimization, approximation, and complexity classes
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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Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
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A design principle for hash functions
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A note on efficient zero-knowledge proofs and arguments (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Conditionally-perfect secrecy and a provably-secure randomized cipher
Journal of Cryptology - Eurocrypt '90
On the theory of average case complexity
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Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
On the existence of statistically hiding bit commitment schemes and fail-stop signatures
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On limited nondeterminism and the complexity of the V-C dimension
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On the Amount of Nondeterminism and the Power of Verifying
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An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Vertex cover: further observations and further improvements
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Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics in Cryptology
Hyper-Encryption and Everlasting Security
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
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CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Separating Random Oracle Proofs from Complexity Theoretic Proofs: The Non-committing Encryption Case
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Unconditional Security Against Memory-Bounded Adversaries
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Replication is not needed: single database, computationally-private information retrieval
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Which Problems Have Strongly Exponential Complexity?
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
A personal view of average-case complexity
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
How to Go Beyond the Black-Box Simulation Barrier
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On the (In)security of the Fiat-Shamir Paradigm
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Foundations of Cryptography: Volume 2, Basic Applications
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The random oracle methodology, revisited
Journal of the ACM (JACM)
Encryption against Storage-Bounded Adversaries from On-Line Strong Extractors
Journal of Cryptology
Optimal Randomizer Efficiency in the Bounded-Storage Model
Journal of Cryptology
On Pseudoentropy versus Compressibility
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Efficient randomized pattern-matching algorithms
IBM Journal of Research and Development - Mathematics and computing
Guest Column: NP-complete problems and physical reality
ACM SIGACT News
On obfuscating point functions
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
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On the randomness complexity of efficient sampling
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Simplifying the weft hierarchy
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Compression of samplable sources
Computational Complexity
Statistical Zero-Knowledge Arguments for NP from Any One-Way Function
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
The PCP theorem by gap amplification
Journal of the ACM (JACM)
Statistically-hiding commitment from any one-way function
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Infeasibility of instance compression and succinct PCPs for NP
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
One-way functions are essential for complexity based cryptography
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Tight lower bounds for certain parameterized NP-hard problems
Information and Computation
Single database private information retrieval implies oblivious transfer
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On everlasting security in the hybrid bounded storage model
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Sufficient conditions for collision-resistant hashing
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Reducing complexity assumptions for statistically-hiding commitment
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Linear kernels in linear time, or how to save k colors in O(n2) steps
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Everlasting security in the bounded storage model
IEEE Transactions on Information Theory
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We study compression that preserves the solution to an instance of a problem rather than preserving the instance itself. Our focus is on the compressibility of $\mathcal{NP}$ decision problems. We consider $\mathcal{NP}$ problems that have long instances but relatively short witnesses. The question is whether one can efficiently compress an instance and store a shorter representation that maintains the information of whether the original input is in the language or not. We want the length of the compressed instance to be polynomial in the length of the witness and polylog in the length of original input. Such compression enables succinctly storing instances until a future setting will allow solving them, either via a technological or algorithmic breakthrough or simply until enough time has elapsed. In this paper, we first develop the basic complexity theory of compression, including reducibility, completeness, and a stratification of $\mathcal{NP}$ with respect to compression. We then show that compressibility (say, of SAT) would have vast implications for cryptography, including constructions of one-way functions and collision resistant hash functions from any hard-on-average problem in $\mathcal{NP}$ and cryptanalysis of key agreement protocols in the “bounded storage model” when mixed with (time) complexity-based cryptography.