STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
On the Composition of Zero-Knowledge Proof Systems
SIAM Journal on Computing
SIAM Journal on Computing
SIAM Journal on Computing
Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Generic Lower Bounds for Root Extraction and Signature Schemes in General Groups
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Sequential Iteration of Interactive Arguments and an Efficient Zero-Knowledge Argument for NP
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Does Parallel Repetition Lower the Error in Computationally Sound Protocols?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Non-Malleable Non-Interactive Zero Knowledge and Adaptive Chosen-Ciphertext Security
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Universal Arguments and their Applications
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Error Reduction by Parallel Repetition—A Negative Result
Combinatorica
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
An efficient parallel repetition theorem for Arthur-Merlin games
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Adaptive One-Way Functions and Applications
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Probabilistic Proof Systems: A Primer
Foundations and Trends® in Theoretical Computer Science
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
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
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
General hardness amplification of predicates and puzzles
TCC'11 Proceedings of the 8th conference on Theory of cryptography
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Parallel repetition for leakage resilience amplification revisited
TCC'11 Proceedings of the 8th conference on Theory of cryptography
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
Counterexamples to hardness amplification beyond negligible
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
A Parallel Repetition Theorem for Constant-Round Arthur-Merlin Proofs
ACM Transactions on Computation Theory (TOCT)
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Parallel repetition is well known to reduce the error probability at an exponential rate for single- and multi-prover interactive proofs. Bellare, Impagliazzo and Naor (1997) show that this is also true for protocols where the soundness only holds against computationally bounded provers (e.g. interactive arguments) if the protocol has at most three rounds. On the other hand, for four rounds they give a protocol where this is no longer the case: the error probability does not decrease below some constant even if the protocol is repeated a polynomial number of times. Unfortunately, this protocol is not very convincing as the communication complexity of each instance of the protocol grows linearly with the number of repetitions, and for such protocols the error does not even decrease for some types of interactive proofs. Noticing this, Bellare et al. construct (a quite artificial) oracle relative to which a four round protocol exists whose communication complexity does not depend on the number of parallel repetitions. This shows that there is no "black-box" error reduction theorem for four round protocols. In this paper we give the first computationally sound protocol where k-fold parallel repetition does not decrease the error probability below some constant for any polynomial k (and where the communication complexity does not depend on k). The protocol has eight rounds and uses the universal arguments of Barak and Goldreich (2001). We also give another four round protocol relative to an oracle, unlike the artificial oracle of Bellare et al., we just need a generic group. This group can then potentially be instantiated with some real group satisfying some well defined hardness assumptions (we do not know of any candidate for such a group at the moment).