Non-interactive and non-malleable commitment
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Black-box concurrent zero-knowledge requires \tilde {Ω} (logn) rounds
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Concurrent zero-knowledge with timing, revisited
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A Cryptographic Solution to a Game Theoretic Problem
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
A Note on the Round-Complexity of Concurrent Zero-Knowledge
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Magic Functions: In Memoriam: Bernard M. Dwork 1923--1998
Journal of the ACM (JACM)
The Complexity of Online Memory Checking
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Foundations of cryptography: a primer
Foundations and Trends® in Theoretical Computer Science
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
The complexity of online memory checking
Journal of the ACM (JACM)
Security Amplification for Interactive Cryptographic Primitives
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Parallel repetition of computationally sound protocols revisited
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Resettable zero-knowledge in the weak public-key model
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
CAPTCHA: using hard AI problems for security
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
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
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
On round-efficient argument systems
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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
Hardness amplification of weakly verifiable puzzles
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Concurrent zero-knowledge with timing, revisited
Theoretical Computer Science
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
On the Composition of Public-Coin Zero-Knowledge Protocols
SIAM Journal on Computing
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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Whether or not parallel repetition lowers the error has been a fundamental question in the theory of protocols, with applications in many different areas. It is well known that parallel repetition reduces the error at an exponential rate in interactive proofs and Arthur-Merlin games. It seems to have been taken for granted that the same is true in arguments, or other proofs where the soundness only holds with respect to computationally bounded parties. We show that this is not the case. Surprisingly, parallel repetition can actually fail in this setting. We present four-round protocols whose error does not decrease under parallel repetition. This holds for any (polynomial) number of repetitions. These protocols exploit non-malleable encryption and can be based on any trapdoor permutation. On the other hand we show that for three-round protocols the error does go down exponentially fast. The question of parallel error reduction is particularly important when the protocol is used in cryptographic settings like identification, and the error represent the probability that an intruder succeeds.