### Abstract

The Rényi divergence is a measure of closeness of two probability distributions. We show that it can often be used as an alternative to the statistical distance in security proofs for lattice-based cryptography. Using the Rényi divergence is particularly suited for security proofs of primitives in which the attacker is required to solve a search problem (e.g., forging a signature). We show that it may also be used in the case of distinguishing problems (e.g., semantic security of encryption schemes), when they enjoy a public sampleability property. The techniques lead to security proofs for schemes with smaller parameters, and sometimes to simpler security proofs than the existing ones.

Original language | English |
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Pages (from-to) | 610-640 |

Number of pages | 31 |

Journal | Journal of Cryptology |

Volume | 31 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 2018 |

### Keywords

- Lattice-based cryptography
- Renyi divergence
- Security proofs
- Statistical distance

## Cite this

*Journal of Cryptology*,

*31*(2), 610-640. https://doi.org/10.1007/s00145-017-9265-9