Ring learning with errors key exchange: Difference between revisions

Revision as of 03:33, 12 October 2023

Latest revision as of 23:09, 30 August 2024

(One intermediate revision by one other user not shown)

Line 37:

== The key exchange ==

The key exchange will take place between two devices. There will be an initiator for the key exchange designated as (I) and a respondent designated as (R). Both I and R know ''q'', ''n'', ''a''(''x''), and have the ability to generate small polynomials according to the distribution <math>\chi_\alpha</math> with parameter <math>\alpha</math>. The distribution <math>\chi_\alpha</math> is usually the discrete Gaussian distribution on the ring <math> R_q = ZqZ_q[x]/\Phi(x)</math>. The description which follows does not contain any explanation of why the key exchange results in the same key at both ends of a link. Rather, it succinctly specifies the steps to be taken. For a thorough understanding of why the key exchange results in the initiator and responder having the same key, the reader should look at the referenced work by Ding et al.<ref name=":0" />

The key exchange begins with the initiator (I) doing the following:

Line 89:

== Key exchange security ==

The security of this key exchange is based on the underlying hardness of [[ring learning with errors]] problem that has been proven to be as hard as the worst case solution to the [[shortest vector problem]] (SVP) in an [[ideal lattice cryptography|ideal lattice]].<ref name=":4" /><ref name=":0" /> The best method to gauge the practical security of a given set of lattice parameters is the BKZ 2.0 lattice reduction algorithm.<ref>{{Cite book|title = BKZ 2.0: Better Lattice Security Estimates|publisher = Springer Berlin Heidelberg|date = 2011|isbn = 978-3-642-25384-3|pages = 1–20|series = Lecture Notes in Computer Science|first1 = Yuanmi|last1 = Chen|first2 = Phong Q.|last2 = Nguyen| title=Advances in Cryptology – ASIACRYPT 2011 | chapter=BKZ 2.0: Better Lattice Security Estimates | volume=7073 |editor-first = Dong Hoon|editor-last = Lee|editor-first2 = Xiaoyun|editor-last2 = Wang|doi = 10.1007/978-3-642-25385-0_1}}</ref> According to the BKZ 2.0 algorithm the key exchange parameters listed above will provide greater than 128 or 256 bits of security, respectively.

==Implementations==