One-way functions and Pseudorandom generators
Combinatorica - Theory of Computing
One-way functions are necessary and sufficient for secure signatures
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Does Parallel Repetition Lower the Error in Computationally Sound Protocols?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Key agreement from weak bit agreement
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
Approximately List-Decoding Direct Product Codes and Uniform Hardness Amplification
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Statistically-hiding commitment from any one-way function
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
An efficient parallel repetition theorem for Arthur-Merlin games
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Uniform direct product theorems: simplified, optimized, and derandomized
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
One-way functions are essential for complexity based cryptography
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Oblivious-Transfer Amplification
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
The uniform hardcore lemma via approximate Bregman projections
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Security Amplification for Interactive Cryptographic Primitives
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Chernoff-Type Direct Product Theorems
Journal of Cryptology
A Parallel Repetition Theorem for Any Interactive Argument
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Parallel repetition of computationally sound protocols revisited
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Degradation and amplification of computational hardness
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Efficiency improvements in constructing pseudorandom generators from one-way functions
Proceedings of the forty-second ACM symposium on Theory of computing
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
Hardness amplification of weakly verifiable puzzles
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
On the power of the randomized iterate
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
A Parallel Repetition Theorem for Constant-Round Arthur-Merlin Proofs
ACM Transactions on Computation Theory (TOCT)
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We give new proofs for the hardness amplification of efficiently samplable predicates and of weakly verifiable puzzles which generalize to new settings. More concretely, in the first part of the paper, we give a new proof of Yao's XOR-Lemma that additionally applies to related theorems in the cryptographic setting. Our proof seems simpler than previous ones, yet immediately generalizes to statements similar in spirit such as the extraction lemma used to obtain pseudo-random generators from one-way functions [Håstad, Impagliazzo, Levin, Luby, SIAM J. on Comp. 1999]. In the second part of the paper, we give a new proof of hardness amplification for weakly verifiable puzzles, which is more general than previous ones in that it gives the right bound even for an arbitrary monotone function applied to the checking circuit of the underlying puzzle. Both our proofs are applicable in many settings of interactive cryptographic protocols because they satisfy a property that we call "non-rewinding". In particular, we show that any weak cryptographic protocol whose security is given by the unpredictability of single bits can be strengthened with a natural information theoretic protocol. As an example, we show how these theorems solve the main open question from [Halevi and Rabin, TCC2008] concerning bit commitment.