Average case complete problems
SIAM Journal on Computing
On the theory of average case complexity
Journal of Computer and System Sciences
Non-interactive and non-malleable commitment
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
SIAM Journal on Computing
Efficient Amplification of the Security of Weak Pseudo-random Function Generators
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Does Parallel Repetition Lower the Error in Computationally Sound Protocols?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Time-lock Puzzles and Timed-release Crypto
Time-lock Puzzles and Timed-release Crypto
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
No better ways to generate hard NP instances than picking uniformly at random
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
CAPTCHA: using hard AI problems for security
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
An efficient parallel repetition theorem for Arthur-Merlin games
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Security Amplification for Interactive Cryptographic Primitives
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Security Notions and Generic Constructions for Client Puzzles
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Chernoff-type direct product theorems
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
HB#: increasing the security and efficiency of HB+
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Degradation and amplification of computational hardness
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Constructive proofs of concentration bounds
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Distinguishing distributions using Chernoff information
ProvSec'10 Proceedings of the 4th international conference on Provable security
Stronger difficulty notions for client puzzles and denial-of-service-resistant protocols
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
General hardness amplification of predicates and puzzles
TCC'11 Proceedings of the 8th conference on Theory of cryptography
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
An efficient parallel repetition theorem
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Parallel repetition theorems for interactive arguments
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Almost optimal bounds for direct product threshold theorem
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Parallel and concurrent security of the HB and HB+ protocols
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Counterexamples to hardness amplification beyond negligible
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Two protocols for delegation of computation
ICITS'12 Proceedings of the 6th international conference on Information Theoretic Security
A Parallel Repetition Theorem for Constant-Round Arthur-Merlin Proofs
ACM Transactions on Computation Theory (TOCT)
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Is it harder to solve many puzzles than it is to solve just one? This question has different answers, depending on how you define puzzles. For the case of inverting one-way functions it was shown by Yao that solving many independent instances simultaneously is indeed harder than solving a single instance (cf. the transformation from weak to strong one-way functions). The known proofs of that result, however, use in an essential way the fact that for one-way functions, verifying candidate solutions to a given puzzle is easy. We extend this result to the case where solutions are efficiently verifiable only by the party that generated the puzzle. We call such puzzles weakly verifiable. That is, for weakly verifiable puzzles we show that if no efficient algorithm can solve a single puzzle with probability more than ε, then no efficient algorithm can solve n independent puzzles simultaneously with probability more than εn. We also demonstrate that when the puzzles are not even weakly verifiable, solving many puzzles may be no harder than solving a single one. Hardness amplification of weakly verifiable puzzles turns out to be closely related to the reduction of soundness error under parallel repetition in computationally sound arguments. Indeed, the proof of Bellare, Impagliazzo and Naor that parallel repetition reduces soundness error in three-round argument systems implies a result similar to our first result, albeit with considerably worse parameters. Also, our second result is an adaptation of their proof that parallel repetition of four-round systems may not reduce the soundness error.