RT Journal Article
T1 Revisiting multivariate ring learning with errors and Its applications on lattice-based cryptography
A1 Pedrouzo Ulloa, Alberto
A1 Troncoso Pastoriza, Juan Ramón
A1 Gama, Nicolas
A1 Georgieva, Mariya
A1 Perez Gonzalez, Fernando
K1 1201 Álgebra
K1 3304 Tecnología de Los Ordenadores
K1 1203.17 Informática
AB 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.
PB Mathematics
SN 22277390
YR 2021
FD 2021-04-14
LK http://hdl.handle.net/11093/2112
UL http://hdl.handle.net/11093/2112
LA eng
NO Mathematics, 9(8): 858 (2021)
NO Agencia Estatal de Investigación (España) | Ref. PID2019-105717RB-C21
DS Investigo
RD 03-oct-2024