Improved cryptanalysis of a ElGamal Cryptosystem Based on Matrices Over Group Rings

Journal of mathematical cryptology

article

Atul Pandey¹  Indivar Gupta²  Dhiraj Kumar Singh³ 

[1] Department of Mathematics, University of Delhi;SAG, Metcalfe House, DRDO Complex;Zakir Husain College, University of Delhi

关键词: Group ring decomposition;    ElGamal cryptosystem;    circulant matrices;   

DOI  :  10.1515/jmc-2019-0054

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

ElGamal cryptosystem has emerged as one of the most important construction in Public Key Cryptography (PKC) since Diffie-Hellman key exchange protocol was proposed. However, public key schemes which are based on number theoretic problems such as discrete logarithm problem (DLP) are at risk because of the evolution of quantum computers. As a result, other non-number theoretic alternatives are a dire need of entire cryptographic community. In 2016, Saba Inam and Rashid Ali proposed a ElGamal-like cryptosystem based on matrices over group rings in ‘Neural Computing & Applications’. Using linear algebra approach, Jia et al. provided a cryptanalysis for the cryptosystem in 2019 and claimed that their attack could recover all the equivalent keys. However, this is not the case and we have improved their cryptanalysis approach and derived all equivalent key pairs that can be used to totally break the ElGamal-like cryptosystem proposed by Saba and Rashid. Using the decomposition of matrices over group rings to larger size matrices over rings, we have made the cryptanalysing algorithm more practical and efficient. We have also proved that the ElGamal cryptosystem proposed by Saba and Rashid does not achieve the security of IND-CPA and IND-CCA.

【 授权许可】

CC BY|CC BY-NC-ND