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Cryptanalysis of an ElGamal-Like Cryptosystem Based on Matrices Over Group Rings

  • Jianwei Jia
  • Houzhen Wang
  • Huanguo Zhang
  • Shijia Wang
  • Jinhui LiuEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 960)

Abstract

ElGamal cryptography is one of the most important Public Key Cryptography (PKC) since Diffie-Hellman exchanges was proposed, however these PKCs which are based on the hard problems that discrete logarithm problem and integer factorization problem are weak with advances in quantum computers. So some alternatives should be proposed. Majid Khan et al. proposed two ElGamal-like public-key encryption schemes based on large abelian subgroup of general linear group over a residue ring, however the two schemes were not long before it was proved unsafe by us. Then, Saba Inam and Rashid (2016) proposed an improved cryptosystem which can resist my attack on “NEURAL COMPUTING & APPLICATIONS”. By analyzing the security of the public key cryptography, we propose an improved method of algebraic key-recovery attack in the polynomial computational complexity despiteing the designers’ claim the cryptosystem is optimal security. Besides, we provide corresponding practical attack example to illustrate the attack method in our cryptanalysis, which breaks instances claiming 80 bits of security less than one minute on a single desktop computer.

Keywords

Cryptography Post-quantum computational cryptography Cryptanalysis Conjugator search problem Computational complexity 

Notes

Acknowledgements

The author would like to thank the anonymous reviewers for their constructive comments and suggestions. This work was supported by National Key R&D Program of China (2017YFB0802000), National Natural Science Foundation of China (61772326, 61572303, 61872229, 61802239), NSFC Research Fund for International Young Scientists (61750110528), National Cryptography Development Fund during the 13th Five-year Plan Period (MMJJ20170216, MMJJ201701304), Foundation of State Key Laboratory of Information Security (2017-MS-03), Fundamental Research Funds for the Central Universities (GK201702004, GK201803061) and China Postdoctoral Science Foundation (2018M631121).

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Jianwei Jia
    • 1
  • Houzhen Wang
    • 2
    • 3
  • Huanguo Zhang
    • 2
    • 3
  • Shijia Wang
    • 4
  • Jinhui Liu
    • 5
    Email author
  1. 1.Huawei Technologies Co., Ltd.Xi’anChina
  2. 2.School of Cyber Science and EngineeringWuhanChina
  3. 3.Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of EducationWuhanChina
  4. 4.Department of Statistics and Actuarial ScienceSimon Fraser UniversityBurnabyCanada
  5. 5.School of Computer ScienceShaanxi Normal UniversityXi’anChina

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