# Probability Preservation Property with Relative Error and Its Applications

### Yuanyuan Gao, Kunpeng Wang

#### Abstract

Probability preservation property plays an important part role in security proofs of lattice based cryptography, which bounds the closeness of two probability distributions. Recent works revolve around different measures. We reform probability preservation properties with relative error which simplify analysis of the security reductions of preimage sampleable functions (PSFs) via different measures and demonstrate R´enyi divergence with order ¥ (RD¥) can coordinate performance with security well. We apply RD¥-based reduction to PSFs over lattices, which reduces the smoothing parameter of Gaussian sampling algorithm by a factor O( p l) without security loss. We further extend the optimized parameter to the secret extraction of identity-based encryption (IBE) over the general lattices by Gentry et al. in STOC 2008 and NTRU lattices proposed by Ducas et al. in Asiacrypt 2014. As a consequence, the size of secret key can be shortened by a factor O( p l) accordingly.

Download#### Paper Citation

#### in Harvard Style

Gao Y. and Wang K. (2018). **Probability Preservation Property with Relative Error and Its Applications**.In *Proceedings of the 4th International Conference on Information Systems Security and Privacy - Volume 1: ICISSP,* ISBN 978-989-758-282-0, pages 461-468. DOI: 10.5220/0006717204610468

#### in Bibtex Style

@conference{icissp18,

author={Yuanyuan Gao and Kunpeng Wang},

title={Probability Preservation Property with Relative Error and Its Applications},

booktitle={Proceedings of the 4th International Conference on Information Systems Security and Privacy - Volume 1: ICISSP,},

year={2018},

pages={461-468},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006717204610468},

isbn={978-989-758-282-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 4th International Conference on Information Systems Security and Privacy - Volume 1: ICISSP,

TI - Probability Preservation Property with Relative Error and Its Applications

SN - 978-989-758-282-0

AU - Gao Y.

AU - Wang K.

PY - 2018

SP - 461

EP - 468

DO - 10.5220/0006717204610468