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

Jintai Ding University of Cincinnati Xiang Xie Chinese Academy of Sciences Xiaodong Lin Rutgers University

TBD mathscidoc:2207.43112

IACR Cryptol. ePrint Arch., 2012.12
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: (x^t \times A)\times y = x^t \times (A\times y), where x,y are column vectors and A 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.
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[ Download ] [ 2022-07-21 15:18:20 uploaded by dingjt ] [ 678 downloads ] [ 0 comments ] 
@inproceedings{jintai2012a,
  title={A Simple Provably Secure Key Exchange Scheme Based on the Learning with Errors Problem},
  author={Jintai Ding, Xiang Xie, and Xiaodong Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220721151820502705694},
  booktitle={IACR Cryptol. ePrint Arch.},
  year={2012},
}
Jintai Ding, Xiang Xie, and Xiaodong Lin. A Simple Provably Secure Key Exchange Scheme Based on the Learning with Errors Problem. 2012. In IACR Cryptol. ePrint Arch.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220721151820502705694.
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