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

Jia, Jianwei; Wang, Houzhen; Zhang, Huanguo; Wang, Shijia; Liu, Jinhui

doi:10.1007/978-981-13-5913-2_16

Cited by 2 publications

(2 citation statements)

References 33 publications

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“…The authors claimed that the cryptosystem is safe against known plaintext attacks and has the potential to resist quantum attacks. But using a linear algebra attack, this proposed cryptosystem was rendered insecure in [5] where the authors also claimed that they could retrieve all the equivalent keys which can be used for decryption. Inam and Ali also provided a simple fix for their cryptosystem which they claimed that it has the ability to defend chosen ciphertext attacks.…”

Section: Introductionmentioning

confidence: 99%

“…Our Contribution: In this paper, we have proved that the ElGamal cryptosystem proposed by Saba and Rashid does not achieve the security of IND-CPA and IND-CCA which makes the cryptosystem completely insecure. We have developed a cryptanalytic attack and derived all equivalent keys (including the keys generated by authors in [5]) that can be used to totally break the ElGamal-like cryptosystem by Saba and Rashid. We have decomposed group ring elements to matrices over base ring and it makes the proposed cryptanalytic algorithm more efficient and practical.…”

Section: Introductionmentioning

confidence: 99%

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

Pandey

Gupta

Singh

2020

Journal of Mathematical Cryptology

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%