STNB2024(37th edition)
On the (Non-)Equivalence of Ring Learning With Errors and Polynomial Learning With Errors
Presenters
Carlo Sanna
Abstract
In this talk, I will briefly introduce the Ring Learning With Errors (RLWE) and the Polynomial Learning With Errors (PLWE) problems (no previous knowledge of lattice-based cryptography is necessary), and explain why their so-called "equivalence" is interesting for cryptographic applications, such as post-quantum cryptography.
Then I will show some results on the equivalence of RLWE and PLWE over cyclotomic number fields, which I obtained in collaboration with Antonio J. Di Scala and Edoardo Signorini. The proofs amount to the study of the condition number of the Vandermonde matrix of the cyclotomic polynomial and employ methods from number theory and linear algebra.
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