Topic
Averaging argument
About: Averaging argument is a research topic. Over the lifetime, 53 publications have been published within this topic receiving 1433 citations.
Papers published on a yearly basis
Papers
8 May 2016
TL;DR: In this article, a zero-knowledge argument for arithmetic circuit satisfiability with a communication complexity that grows logarithmically in the size of the circuit was proposed, where the soundness of the argument relies solely on the well-established discrete log-arm assumption in prime order groups.
Abstract: We provide a zero-knowledge argument for arithmetic circuit satisfiability with a communication complexity that grows logarithmically in the size of the circuit. The round complexity is also logarithmic and for an arithmetic circuit with fan-in 2 gates the computation of the prover and verifier is linear in the size of the circuit. The soundness of our argument relies solely on the well-established discrete logarithm assumption in prime order groups.
At the heart of our new argument system is an efficient zero-knowledge argument of knowledge of openings of two Pedersen multicommitments satisfying an inner product relation, which is of independent interest. The inner product argument requires logarithmic communication, logarithmic interaction and linear computation for both the prover and the verifier.
We also develop a scheme to commit to a polynomial and later reveal the evaluation at an arbitrary point, in a verifiable manner. This is used to build an optimized version of the constant round square root complexity argument of Groth CRYPTO 2009, which reduces both communication and round complexity.
354 citations
Book•
9 Nov 2011TL;DR: This book explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public-key cryptography and describes new interesting developments in the algorithmic theory of solvable groups.
Abstract: This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public-key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory. In particular, a lot of emphasis in the book is put on studying search problems, as compared to decision problems traditionally studied in combinatorial group theory. Then, complexity theory, notably generic-case complexity of algorithms, is employed for cryptanalysis of various cryptographic protocols based on infinite groups, and the ideas and machinery from the theory of generic-case complexity are used to study asymptotically dominant properties of some infinite groups that have been applied in public-key cryptography so far. This book also describes new interesting developments in the algorithmic theory of solvable groups and another spectacular new development related to complexity of group-theoretic problems, which is based on the ideas of compressed words and straight-line programs coming from computer science.
184 citations
Book•
27 Aug 2008
TL;DR: This paper discusses decision problems in Public Key Cryptography, the Asymptotically Dominant Properties of Cryptanalysis, and length-Based and Quotient Attacks.
Abstract: Background on Groups, Complexity, and Cryptography.- Background on Public Key Cryptography.- Background on Combinatorial Group Theory.- Background on Computational Complexity.- Non-commutative Cryptography.- Canonical Non-commutative Cryptography.- Platform Groups.- Using Decision Problems in Public Key Cryptography.- Generic Complexity and Cryptanalysis.- Distributional Problems and the Average-Case Complexity.- Generic Case Complexity.- Generic Complexity of NP-complete Problems.- Asymptotically Dominant Properties and Cryptanalysis.- Asymptotically Dominant Properties.- Length-Based and Quotient Attacks.
116 citations
1 Apr 1988
94 citations
TL;DR: Signature Security: Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem are discussed in this paper, where the authors present a construction without random oracles.
Abstract: Signature Security.- Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem.- Security of Verifiably Encrypted Signatures and a Construction without Random Oracles.- Multisignatures as Secure as the Diffie-Hellman Problem in the Plain Public-Key Model.- Curves.- On the Security of Pairing-Friendly Abelian Varieties over Non-prime Fields.- Generating Pairing-Friendly Curves with the CM Equation of Degree 1.- Pairing Computation.- On the Final Exponentiation for Calculating Pairings on Ordinary Elliptic Curves.- Faster Pairings on Special Weierstrass Curves.- Fast Hashing to G 2 on Pairing-Friendly Curves.- NIZKs and Applications.- Compact E-Cash and Simulatable VRFs Revisited.- Proofs on Encrypted Values in Bilinear Groups and an Application to Anonymity of Signatures.- Group Signatures.- Identity Based Group Signatures from Hierarchical Identity-Based Encryption.- Forward-Secure Group Signatures from Pairings.- Efficient Traceable Signatures in the Standard Model.- Protocols.- Strongly Secure Certificateless Key Agreement.- Universally Composable Adaptive Priced Oblivious Transfer.- Conjunctive Broadcast and Attribute-Based Encryption.
80 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2018 | 1 |
| 2017 | 1 |
| 2016 | 4 |
| 2015 | 2 |
| 2014 | 6 |
| 2013 | 1 |