A Key Exchange Based on the Short Integer Solution Problem and the Learning with Errors Problem

2019 ◽  
pp. 105-117 ◽  
Author(s):  
Jintai Ding ◽  
Kevin Schmitt ◽  
Zheng Zhang
Keyword(s):  
Key Exchange ◽  
Integer Solution ◽  
Learning With Errors ◽  
Learning With Errors Problem ◽  
Solution Problem

Lattice-based key exchange on small integer solution problem

2014 ◽  
Vol 57 (11) ◽  
pp. 1-12 ◽  
Author(s):  
ShanBiao Wang ◽  
Yan Zhu ◽  
Di Ma ◽  
RongQuan Feng
Keyword(s):  
Key Exchange ◽  
Integer Solution ◽  
Small Integer ◽  
Small Integer Solution Problem ◽  
Solution Problem

Cryptanalysis of lattice-based key exchange on small integer solution problem and its improvement

2018 ◽  
Vol 22 (S1) ◽  
pp. 1717-1727
Author(s):  
Zhengjun Jing ◽  
Chunsheng Gu ◽  
Zhimin Yu ◽  
Peizhong Shi ◽  
Chongzhi Gao
Keyword(s):  
Key Exchange ◽  
Integer Solution ◽  
Small Integer ◽  
Small Integer Solution Problem ◽  
Solution Problem

Group authenticated key exchange schemes via learning with errors

2015 ◽  
Vol 8 (17) ◽  
pp. 3142-3156 ◽  
Author(s):  
Xiaopeng Yang ◽  
Wenping Ma ◽  
Chengli Zhang
Keyword(s):  
Key Exchange ◽  
Authenticated Key Exchange ◽  
Learning With Errors

scholarly journals New variant for Learning with Errors Problem

2018 ◽  
Vol 131 ◽  
pp. 502-510
Author(s):  
Xuyang Wang ◽  
Aiqun Hu ◽  
Hao Fang
Keyword(s):  
New Variant ◽  
Learning With Errors ◽  
Learning With Errors Problem

scholarly journals Revisiting Multivariate Ring Learning with Errors and Its Applications on Lattice-Based Cryptography

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 858
Author(s):  
Alberto Pedrouzo-Ulloa ◽  
Juan Ramón Troncoso-Pastoriza ◽  
Nicolas Gama ◽  
Mariya Georgieva ◽  
Fernando Pérez-González
Keyword(s):  
Cyclotomic Polynomials ◽  
Time Efficiency ◽  
Space And Time ◽  
Low Degree ◽  
Learning With Errors ◽  
Lattice Based Cryptography ◽  
Low Degree Polynomials ◽  
Learning With Errors Problem ◽  
Recent Attack

The “Multivariate Ring Learning with Errors” problem was presented as a generalization of Ring Learning with Errors (RLWE), introducing efficiency improvements with respect to the RLWE counterpart thanks to its multivariate structure. Nevertheless, the recent attack presented by Bootland, Castryck and Vercauteren has some important consequences on the security of the multivariate RLWE problem with “non-coprime” cyclotomics; this attack transforms instances of m-RLWE with power-of-two cyclotomic polynomials of degree n=∏ini into a set of RLWE samples with dimension maxi{ni}. This is especially devastating for low-degree cyclotomics (e.g., Φ4(x)=1+x2). In this work, we revisit the security of multivariate RLWE and propose new alternative instantiations of the problem that avoid the attack while still preserving the advantages of the multivariate structure, especially when using low-degree polynomials. Additionally, we show how to parameterize these instances in a secure and practical way, therefore enabling constructions and strategies based on m-RLWE that bring notable space and time efficiency improvements over current RLWE-based constructions.

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