| Texto completo | |
| Autor(es): |
Ortiz, Jheyne N.
[1]
;
de Araujo, Robson R.
[2]
;
Aranha, Diego F.
[3]
;
Costa, Sueli I. R.
[4]
;
Dahab, Ricardo
[1]
Número total de Autores: 5
|
| Afiliação do(s) autor(es): | [1] Univ Estadual Campinas, Inst Comp, BR-13083852 Campinas - Brazil
[2] Fed Inst Sao Paulo, BR-11533160 Cubatao - Brazil
[3] Aarhus Univ, Dept Comp Sci, DK-8200 Aarhus - Denmark
[4] Univ Estadual Campinas, Inst Math Stat & Comp Sci, BR-13083859 Campinas - Brazil
Número total de Afiliações: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Entropy; v. 23, n. 9 SEP 2021. |
| Citações Web of Science: | 0 |
| Resumo | |
Several works have characterized weak instances of the Ring-LWE problem by exploring vulnerabilities arising from the use of algebraic structures. Although these weak instances are not addressed by worst-case hardness theorems, enabling other ring instantiations enlarges the scope of possible applications and favors the diversification of security assumptions. In this work, we extend the Ring-LWE problem in lattice-based cryptography to include algebraic lattices, realized through twisted embeddings. We define the class of problems Twisted Ring-LWE, which replaces the canonical embedding by an extended form. By doing so, we allow the Ring-LWE problem to be used over maximal real subfields of cyclotomic number fields. We prove that Twisted Ring-LWE is secure by providing a security reduction from Ring-LWE to Twisted Ring-LWE in both search and decision forms. It is also shown that the twist factor does not affect the asymptotic approximation factors in the worst-case to average-case reductions. Thus, Twisted Ring-LWE maintains the consolidated hardness guarantee of Ring-LWE and increases the existing scope of algebraic lattices that can be considered for cryptographic applications. Additionally, we expand on the results of Ducas and Durmus (Public-Key Cryptography, 2012) on spherical Gaussian distributions to the proposed class of lattices under certain restrictions. As a result, sampling from a spherical Gaussian distribution can be done directly in the respective number field while maintaining its format and standard deviation when seen in R-n via twisted embeddings. (AU) | |
| Processo FAPESP: | 13/25977-7 - Segurança e confiabilidade da informação: teoria e prática |
| Beneficiário: | Marcelo Firer |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |