Non-interactive zero-knowledge and its applications
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Linear Algebra with Sub-linear Zero-Knowledge Arguments
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Perfect NIZK with adaptive soundness
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Cryptographic primitives enforcing communication and storage complexity
FC'02 Proceedings of the 6th international conference on Financial cryptography
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EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
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ACISP'10 Proceedings of the 15th Australasian conference on Information security and privacy
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Gradual sub-lattice reduction and a new complexity for factoring polynomials
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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Pairing-Friendly elliptic curves of prime order
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IEEE Transactions on Information Theory
A more efficient computationally sound non-interactive zero-knowledge shuffle argument
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Succinct malleable NIZKs and an application to compact shuffles
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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Proceedings of the 8th ACM European Conference on Computer Systems
Recursive composition and bootstrapping for SNARKS and proof-carrying data
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Zero-knowledge using garbled circuits: how to prove non-algebraic statements efficiently
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
Secure equality and greater-than tests with sublinear online complexity
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Rational arguments: single round delegation with sublinear verification
Proceedings of the 5th conference on Innovations in theoretical computer science
A more efficient computationally sound non-interactive zero-knowledge shuffle argument
Journal of Computer Security - Advances in Security for Communication Networks
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In 2010, Groth constructed the only previously known sublinear-communication NIZK circuit satisfiability argument in the common reference string model. We optimize Groth's argument by, in particular, reducing both the CRS length and the prover's computational complexity from quadratic to quasilinear in the circuit size. We also use a (presumably) weaker security assumption, and have tighter security reductions. Our main contribution is to show that the complexity of Groth's basic arguments is dominated by the quadratic number of monomials in certain polynomials. We collapse the number of monomials to quasilinear by using a recent construction of progression-free sets.