## Abstract

Homomorphic encryption (HE) has opened an entirely new world up in the privacy-preserving use of sensitive data by conducting computations on encrypted data. Amongst many HE schemes targeting computation in various contexts, Cheon–Kim–Kim–Song (CKKS) scheme [8] is distinguished since it allows computations for encrypted real number data, which have greater impact in real-world applications. CKKS scheme is a levelled homomorphic encryption scheme, consuming one level for each homomorphic multiplication. When the level runs out, a special computational circuit called bootstrapping is required in order to conduct further multiplications. The algorithm proposed by Cheon et al. [7] has been regarded as a standard way to do bootstrapping in the CKKS scheme, and it consists of the following four steps: ModRaise, CoeffToSlot, EvalMod and SlotToCoeff. However, the steps consume a number of levels themselves, and thus optimizing this extra consumption has been a major focus of the series of recent research. Among the total levels consumed in the bootstrapping steps, about a half of them is spent in CoeffToSlot and SlotToCoeff steps to scale up the real number components of DFT matrices and round them to the nearest integers. Each scale-up factor is very large so that it takes up one level to rescale it down. Scale-up factors can be taken smaller to save levels, but the error of rounding would be transmitted to EvalMod and eventually corrupt the accuracy of bootstrapping. EvalMod aims to get rid of the superfluous qI term from a plaintext pt+ qI resulting from ModRaise, where q is the bottom modulus and I is a polynomial with small integer coefficients. EvalRound is referred to as its opposite, obtaining qI. We introduce a novel bootstrapping algorithm consisting of ModRaise, CoeffToSlot, EvalRound and SlotToCoeff, which yields taking smaller scale-up factors without the damage of rounding errors.

Original language | English |
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Title of host publication | Advances in Cryptology – ASIACRYPT 2022 - 28th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings |

Editors | Shweta Agrawal, Dongdai Lin |

Publisher | Springer Science and Business Media Deutschland GmbH |

Pages | 161-187 |

Number of pages | 27 |

ISBN (Print) | 9783031229657 |

DOIs | |

State | Published - 2022 |

Event | 28th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2022 - Taipei, Taiwan, Province of China Duration: 5 Dec 2022 → 9 Dec 2022 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 13792 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 28th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2022 |
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Country/Territory | Taiwan, Province of China |

City | Taipei |

Period | 5/12/22 → 9/12/22 |

## Keywords

- Bootstrapping
- CKKS scheme
- Homomorphic encryption