Design and Simulation of d Dimensional (t,n) Threshold Quantum Homomorphic Encryption Algorithm

SONG Xiu-li; ZHOU Dao-yang; WEN Ai-jun

doi:10.3969/j.issn.0372-2112.2020.05.003

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Design and Simulation of d Dimensional (t,n) Threshold Quantum Homomorphic Encryption Algorithm

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- Design and Simulation of d Dimensional (t,n) Threshold Quantum Homomorphic Encryption Algorithm
- Acta Electronica Sinica Vol. 48, Issue 5, Pages: 846-853(2020)
- 作者机构：
  
  1. 重庆邮电大学网络空间安全与信息法学院,重庆,400065
  2. 重庆邮电大学计算机科学与技术学院,重庆,400065
  3. 重庆邮电大学网络空间安全与信息法学院,重庆,400065
  4. 重庆邮电大学计算机科学与技术学院,重庆,400065
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61772098, No.61772099, No.61802039);Basic and Frontier Research Program of Chongqing Municipal Science and Technology Commission (No.cstc2018jcyjAX0510)
- DOI：10.3969/j.issn.0372-2112.2020.05.003
  CLC： TP309
- Published Online：25 May 2020，
  
  Published：2020
- 稿件说明：
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SONG Xiu-li, ZHOU Dao-yang, WEN Ai-jun. Design and Simulation of d Dimensional (t,n) Threshold Quantum Homomorphic Encryption Algorithm[J]. Acta Electronica Sinica, 2020, 48(5): 846-853.
DOI：

SONG Xiu-li, ZHOU Dao-yang, WEN Ai-jun. Design and Simulation of d Dimensional (t,n) Threshold Quantum Homomorphic Encryption Algorithm[J]. Acta Electronica Sinica, 2020, 48(5): 846-853. DOI： 10.3969/j.issn.0372-2112.2020.05.003.

摘要

量子同态加密对量子态密文直接进行同态评估计算，而不是将密文解密之后再进行计算.基于相位和状态变换的

维通用酉算子，提出了一种

维（

t，n

）门限量子同态加密算法.在该算法中，客户端将量子态密文传送给

个服务器中的

个，这

个服务器生成评估子密钥，运行评估算法对量子态密文执行同态计算.客户端对解密之后的量子态执行CNOT门操作，

+1个粒子的聚合值就是评估算法对量子态明文计算之后的结果.该算法使用Shamir（

t，n

）门限机制隐藏了评估密钥，保护了客户端的隐私数据.从理论上证明了算法的正确性，各个阶段操作过程的仿真实现进一步验证了算法的正确性.

Abstract

Quantum homomorphic cryptography directly evaluates the quantum ciphertext

rather than decrypts the quantum ciphertext and then calculates it. Based on a general

-dimensional unitary operator of phase and state transformation

-dimensional (

) threshold quantum homomorphic encryption algorithm was proposed. In this algorithm

the client sent the quantum state ciphertext to

servers. Each of the

servers generated the evaluation sub-keys

and then run the evaluation algorithm on the quantum state ciphertext to complete the calculation of quantum homomorphism. The client perfo

rmed CNOT gates on the quantum states after decryption

and the aggregate value of

+1 particles was the result after evaluation calculation on the quantum state plaintext. The algorithm uses Shamir's (

) threshold scheme to hide the evaluation keys

so that it protects the client's private data. The theorems prove the correctness of the algorithm theoretically

and the simulations of each stage of the algorithm further verify its correctness.

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School of Cyber Security and Information Law, Chongqing University of Posts and Telecommunications

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