How to validate the secret of a Ring Learning with Errors (RLWE) key

Jintai Ding University of Cincinnati Saraswathy RV University of Cincinnati Saed Alsayigh University of Cincinnati Crystal Clough University of Cincinnati

TBD mathscidoc:2207.43122

IACR Cryptol. ePrint Arch., 2018.1
We use the signal function from RLWE key exchange to derive an efficient zero knowledge authentication protocol to validate an RLWE key p=as+e with secret s and error e in the Random Oracle Model (ROM). With this protocol, a verifier can validate that a key presented to him by a prover P is of the form p=as+e with s,e small and that the prover knows s. We accompany the description of the protocol with proof to show that it has negligible soundness and completeness error. The soundness of our protocol relies directly on the hardness of the RLWE problem. The protocol is applicable for both LWE and RLWE but we focus on the RLWE based protocol for efficiency and practicality. We also present a variant of the main protocol with a commitment scheme to avoid using the ROM.
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@inproceedings{jintai2018how,
  title={How to validate the secret of a Ring Learning with Errors (RLWE) key},
  author={Jintai Ding, Saraswathy RV, Saed Alsayigh, and Crystal Clough},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220722170154843571705},
  booktitle={IACR Cryptol. ePrint Arch.},
  year={2018},
}
Jintai Ding, Saraswathy RV, Saed Alsayigh, and Crystal Clough. How to validate the secret of a Ring Learning with Errors (RLWE) key. 2018. In IACR Cryptol. ePrint Arch.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220722170154843571705.
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