1. What are the contributions in "The kernel matrix diffie-hellman assumption" ?
The authors show that for any such family of MDDH assumptions, the corresponding Kernel assumptions are also strictly increasingly weaker.
read more
The Kernel Matrix Diffie-Hellman assumption
Paz Morillo,Carla Ràfols,Jorge L. Villar +2 more
- 04 Dec 2016
- Vol. 10031, pp 729-758
TL;DR: A new family of computational assumptions, the Kernel Matrix Diffie-Hellman Assumption, is put forward, which allows to extend the advantages of their algebraic framework to computational assumptions.
read more
Abstract: We put forward a new family of computational assumptions, the Kernel Matrix Diffie-Hellman Assumption. Given some matrix \(\mathbf {{A}}\) sampled from some distribution \(\mathcal {D}\), the kernel assumption says that it is hard to find “in the exponent” a nonzero vector in the kernel of \(\mathbf {{A}}^\top \). This family is a natural computational analogue of the Matrix Decisional Diffie-Hellman Assumption (MDDH), proposed by Escala et al. As such it allows to extend the advantages of their algebraic framework to computational assumptions.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Most frequently asked questions
Figures
Citations
The Algebraic Group Model and its Applications
Georg Fuchsbauer,Eike Kiltz,Julian Loss +2 more
- 19 Aug 2018
TL;DR: The Generic Group Model (GGM) is one of the most important and successful tools for assessing hardness assumptions in cryptography and has been used extensively in the past two decades.
Advances in Cryptology – ASIACRYPT 2016
Jung Hee Cheon,Tsuyoshi Takagi +1 more
- 01 Jan 2016
TL;DR: This talk will provide a brief introduction to functional encryption and an overview of the state of the art, with a focus on constructions based on lattices.
46
More Efficient (Almost) Tightly Secure Structure-Preserving Signatures
Dennis Hofheinz,Lisa Kohl,Jiaxin Pan +2 more
- 29 Apr 2018
TL;DR: Abe et al. as mentioned in this paper proposed a structure-preserving signature (SPS) scheme with an almost tight security reduction to a standard assumption, which has smaller signatures and public keys.
Efficient Zero-Knowledge Arguments in the Discrete Log Setting, Revisited
Max Hoffmann,Michael Klooß,Andy Rupp +2 more
- 06 Nov 2019
TL;DR: This work revisits zero-knowledge proofs in the discrete logarithm setting, and identifies and carve out basic techniques to optimise proofs in this setting, demonstrating that general quadratic constraints, not just R1CS, are a natural relation in the dlog (or ideal linear commitment) setting.
44
Shorter Non-interactive Zero-Knowledge Arguments and ZAPs for Algebraic Languages
Geoffroy Couteau,Dominik Hartmann +1 more
- 17 Aug 2020
TL;DR: This work puts forth a new framework for building pairing-based non-interactive zero-knowledge arguments for a wide class of algebraic languages, which are an extension of linear languages, containing disjunctions oflinear languages and more.
References
Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing
Torben P. Pedersen
- 11 Aug 1991
TL;DR: It is shown how to distribute a secret to n persons such that each person can verify that he has received correct information about the secret without talking with other persons.
2.9K
Efficient identity-based encryption without random oracles
Brent Waters
- 22 May 2005
TL;DR: This work first presents their IBE construction and reduces the security of the scheme to the decisional Bilinear Diffie-Hellman (BDH) problem, and shows that their techniques can be used to build a new signature scheme that is secure under the computational Diffie -Hellman assumption without random oracles.
Short Group Signatures
Dan Boneh,Xavier Boyen,Hovav Shacham +2 more
- 15 Aug 2004
TL;DR: In this article, the authors proposed a group signature scheme based on the Strong Diffie-Hellman assumption and a new assumption in bilinear groups called the Decision Linear assumption.
•Journal Article
Short group signatures
TL;DR: In this paper, the authors proposed a group signature scheme based on the Strong Diffie-Hellman assumption and a new assumption in bilinear groups called the Decision Linear assumption.
1.5K
Untraceable off-line cash in wallet with observers
Stefan A. Brands
- 02 Jan 1994
TL;DR: The electronic cash scheme in [Fer93a] can be extended to provide n-spendable coins and observers can be incorporated in the protocols to provide prior restraint against double spending by the user, instead of just detection after the fact.
Related Papers (5)
Eike Kiltz,Hoeteck Wee +1 more
- 26 Apr 2015
Charanjit S. Jutla,Arnab Roy +1 more
- 01 Dec 2013
Jens Groth,Amit Sahai +1 more
- 13 Apr 2008