LWE from non-commutative group rings
| Autor: | Qi Cheng, Jun Zhang, Jincheng Zhuang |
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| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Discrete mathematics Computer Science - Cryptography and Security Mathematics::Commutative Algebra Group (mathematics) Applied Mathematics Lattice problem Dihedral group Computer Science Applications Lattice (module) Ideal (ring theory) Abelian group Semantic security Cryptography and Security (cs.CR) Computer Science::Cryptography and Security Mathematics Group ring |
| Zdroj: | Designs, Codes and Cryptography. 90:239-263 |
| ISSN: | 1573-7586 0925-1022 |
| DOI: | 10.1007/s10623-021-00973-6 |
| Popis: | The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptography. There are however recent discoveries of faster algorithms for the principal ideal SVP problem, and attempts to generalize the attack to non-principal ideals. In this work, we study the LWE problem on group rings, and build cryptographic schemes based on this new primitive. One can regard the LWE on cyclotomic integers as a special case when the underlying group is cyclic, while our proposal utilizes non-commutative groups, which eliminates the weakness associated with the principal ideal lattices. In particular, we show how to build public key encryption schemes from dihedral group rings, which maintains the efficiency of the ring-LWE and improves its security. A refined security analysis is provided |
| Databáze: | OpenAIRE |
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