A Simple Provably Secure Key Exchange Scheme Based on the Learning with Errors Problem

Jintai Ding; Xiang Xie; Xiaodong Lin

Paper 2012/688

A Simple Provably Secure Key Exchange Scheme Based on the Learning with Errors Problem

Jintai Ding, Xiang Xie, and Xiaodong Lin

Abstract

We use the learning with errors (LWE) problem to build a new simple and provably secure key exchange scheme. The basic idea of the construction can be viewed as certain extension of Diffie-Hellman problem with errors. The mathematical structure behind comes from the commutativity of computing a bilinear form in two different ways due to the associativity of the matrix multiplications: where are column vectors and is a square matrix. We show that our new schemes are more efficient in terms of communication and computation complexity compared with key exchange schemes or key transport schemes via encryption schemes based on the LWE problem. Furthermore, we extend our scheme to the ring learning with errors (RLWE) problem, resulting in small key size and better efficiency.

Note: The security proof is added and this version of the paper was submitted to Eurocrypt 2014.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown status
Keywords: Key Exchange Diffie-Hellmann LWE
Contact author(s): jintai ding @ gmail com
History: 2014-07-29: last of 4 revisions; 2012-12-10: received; See all versions
Short URL: https://ia.cr/2012/688
License: CC BY

BibTeX

@misc{cryptoeprint:2012/688,
      author = {Jintai Ding and Xiang Xie and Xiaodong Lin},
      title = {A Simple Provably Secure Key Exchange Scheme Based on the Learning with Errors Problem},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/688},
      year = {2012},
      url = {https://eprint.iacr.org/2012/688}
}