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Revisiting Multivariate Ring Learning with Errors and its Applications on Lattice-based Cryptography [article]

Alberto Pedrouzo-Ulloa, Juan Ramón Troncoso-Pastoriza, Nicolas Gama, Mariya Georgieva, Fernando Pérez-González
2019 IACR Cryptology ePrint Archive  
This is especially devastating for low-degree cyclotomics (e.g., Φ 4 (x) = 1 + x 2 ).  ...  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  ...  fundamental lattice operations (faster polynomial multiplications through α-generalized Walsh-Hadamard Transforms), efficient cryptographic operations such as computation of automorphisms, relinearizations  ... 
dblp:journals/iacr/Pedrouzo-UlloaT19 fatcat:y45ql43vfvgljnjchl22riej5e

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

Alberto Pedrouzo-Ulloa, Juan Ramón Troncoso-Pastoriza, Nicolas Gama, Mariya Georgieva, Fernando Pérez-González
2021 Mathematics  
This is especially devastating for low-degree cyclotomics (e.g., Φ4(x)=1+x2).  ...  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  ...  Reprinted, with permission, from Sections 3 and 4 of the conference paper: "Multiquadratic Rings and Walsh-Hadamard Transforms for Oblivious Linear Function Evaluation", 2020 IEEE International Workshop  ... 
doi:10.3390/math9080858 fatcat:b3vbn777wjb5texfvbuedcnaui