# Fully Homomorphic Encryption without bootstrapping

@article{Yagisawa2015FullyHE, title={Fully Homomorphic Encryption without bootstrapping}, author={Masahiro Yagisawa}, journal={IACR Cryptol. ePrint Arch.}, year={2015}, volume={2015}, pages={474} }

Fully homomorphic encryption(FHE) is the cryptosystem which supports both addition and multiplication. The existence of the cryptosystems which have efficiency and fully homomorphism would bring great practical implications in the outsourcing of private computations, for instance, in the context of cloud computing. But FHE scheme which runs fast for practical use is not proposed until now because the scheme requires huge complexity. This book, therefore, provides the new fully homomorphic…

## 263 Citations

### Fully Homomorphic Encryption on Octonion Ring

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2015

The improved fully homomorphic encryption scheme on non-associative octonion ring over finite field without bootstrapping technique is proposed, based on multivariate algebraic equations with high degree or too many variables while the almost all multivariate cryptosystems proposed until now are based on the quadratic equations avoiding the explosion of the coefficients.

### Homomorphic encryption 2 1 Introduction

- Computer Science, Mathematics
- 2016

This document describes the construction under the assumption that the approximate GCD problem is hard and shows how to build somewhat homomorphic encryption (SHE) based on the learning with errors (LWE) problem, which can be used to evaluate a restricted class of algorithms over encrypted data.

### Improved fully homomorphic public-key encryption with small ciphertext size

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2018

This paper proposes the fully homomorphic public-key encryption scheme with the size of ciphertext which is not small enough, and adopts the medium text with zero norm, and is immune from the Gröbner basis attack, the differential attack, rank attack and so on.

### Fully Homomorphic Public-Key Encryption Against Ciphertext Square Attack with Two Ciphertexts

- Computer Science, Mathematics
- 2018

A new FHPKE against "ciphertext square attack" is proposed which does not need the bootstrapping and does not require the large complexity for enciphering and it is shown that proposed system is immune from “cipher Text square attack’, “m and -m attack” and the Grobner basis attacks.

### Fully Homomorphic Encryption: A Case Study

- Computer Science, Mathematics
- 2018

This thesis is survey on FHE and MKFHE, with special attention to the state of the art implementations available as well as three implementations including the first implementation in the multi-key settings to the best of the authors' knowledge.

### Improved Fully Homomorphic Encryption without Bootstrapping

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2017

The improved fully homomorphic public-key encryption scheme on non-associative octonion ring over finite field without bootstrapping technique is proposed, which is against the Gröbner basis attack, the differential attack, rank attack and so on.

### Fully Homomorphic Encryption with Composite Number Modulus

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2015

This paper proposes the improved fully homomorphic encryption scheme on non-associative octonion ring over finite ring with composite number modulus where the plaintext p consists of three numbers u,v,w and it is proved that if there exists the PPT algorithm that decrypts the plain Text from the ciphertexts of the proposed scheme, there exist the P PT algorithm that factors the given composite numbermodulus.

### Improved Fully Homomorphic Encryption with Composite Number Modulus

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2016

Another fully homomorphic encryption with composite number modulus where the complexity required for enciphering and deciphering is smaller than the same modulus RSA scheme and is immune from the “p and -p attack”.

### Minimizing the Number of Bootstrappings in Fully Homomorphic Encryption

- Mathematics, Computer ScienceSAC
- 2015

It is proved that the problem of minimizing bootstrapping is NP-complete with a reduction from a graph problem and a flexible technique is proposed that permits to determine both such minimal number of bootstrappings and where to place them in the circuit.

### On FHE Without Bootstrapping ( Informal )

- Computer Science, Mathematics
- 2013

This work proposes an IND-CPA secure symmetric key homomorphic encryption scheme using multivariate polynomial ring over finite fields and gives a method of constructing a CPA secure homomorphicryption scheme from another symmetric deterministic CPASecure scheme.

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- 2015