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Special Issue: Theory and Algorithms

• Theory and Algorithms •

### Generalized Goldwasser and Micali's Type Cryptosystem

Ying Guo1 (郭莹), Zhen-Fu Cao2,3,4,* (曹珍富), Senior Member, IEEE, Member, CCF, and Xiao-Lei Dong2 (董晓蕾), Member, IEEE

1. 1Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
2Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China
3Cyberspace Security Research Center, Peng Cheng Laboratory, Shenzhen 518055, China
4Institute of Intelligent Science and Technology, Tongji University, Shanghai 200092, China
• Received:2020-07-16 Revised:2021-04-26 Accepted:2021-04-29 Online:2022-03-31 Published:2022-03-31
• Contact: Zhen-Fu Cao E-mail:zfcao@sei.ecnu.edu.cn
• About author:Zhen-Fu Cao is currently a distinguished professor in Shanghai Key Laboratory of Trustworthy Computing in East China Normal University, Shanghai. He received his Ph.D. degree in the Harbin Institute of Technology, Harbin, in 1999. His research interests mainly include number theory, cryptography, and information security. He is a member of CCF and a senior member of IEEE.
• Supported by:
The work was supported by the National Key Research and Development Program of China under Grant No. 2020YFA0712300, the National Natural Science Foundation of China under Grant No. 61632012, and the Peng Cheng Laboratory Project of Guangdong Province of China under Grant No. PCL2018KP004.

In 1982, Goldwasser and Micali proposed the first probabilistic public key cryptosystem with indistinguishability under chosen plaintext attack security based on the quadratic residuosity assumption. Ciphertext expansion of Goldwasser's scheme is quite large, thereby the scheme is inefficient. A lot of schemes have been proposed to reduce the ciphertext expansion. Some schemes use the same encryption algorithm as Goldwasser's scheme with different parameters and keys, which we call them Goldwasser and Micali's type (GM-type) schemes. GM-type schemes can be divided into two categories according to different parameters and decryption algorithms. In this paper, we propose the first generalized GM-type scheme combining these two categories. All GM-type schemes are special cases of our generalized GM-type scheme. The ciphertext expansion of our scheme is smaller than that of any other GM-type schemes.

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