Subject: I-D Action: draft-cfrg-khera-lpr-ring-lwe-kex-00.txt

From: [email-masked]
Date: Tue, 24 Oct 2017 12:12:25 -0700

A New Internet-Draft is available from the on-line Internet-Drafts directories.

        Title           : Post-Quantum Key Exchange From Learning With Errors Over Rings
        Author          : Rohit Khera
	Filename        : draft-cfrg-khera-lpr-ring-lwe-kex-00.txt
	Pages           : 36
	Date            : 2017-10-24

Abstract:
     This note describes a key exchange method based on the ring-LWE
     (RLWE) assumption. It builds upon several results, including
     Regev's landmark quantum reduction from certain worst case lattice
     problems (approx. GapSVP and SIVP) to random instances of the
     search variant of a particular learning problem (LWE). It also
     builds on the follow on work of Lyubashevsky, Peikert and Regev on
     the average case hardness of the RLWE search variant for
     polynomially bounded numbers of RLWE samples, along with novel
     applications of automorphism groups in number fields for a RLWE
     search to decision reduction (thereby demonstrating
     pseudorandomness of RLWE in these number fields). Subsequently,
     these results were adopted for the construction of Diffie-Hellman
     like key exchange methods by Peikert, and then by Lindner and
     Peikert followed by Ding and then by Ding, Xie and Lin who proposed
     efficient variants of such protocols. Subsequent work by Peikert
     proposed another efficient variant, phrased as a key encapsulation
     method, incorporating a low bandwidth "reconciliation" technique
     allowing two parties to exactly agree on a uniformly distributed
     secret value from noisy RLWE instances. This was followed by a
     concrete instantiation with parameter sets by Bos, Costello,
     Naehrig, Stebila, followed by another instantiation by Alkim,
     Ducas, Poppelmann and Schwabe with the same ring polynomial but a
     smaller modulus and a different reconciliation method. Unlike most
     other public key cryptography based key exchange methods, it is
     believed that RLWE based key exchange would remain secure in the
     event that an adversary is able to build a quantum computer.

     This document is a product of the Crypto Forum Research Group
     (CFRG).

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