LWE from non-commutative group rings

Cheng, Qi; Zhang, Jun; Zhuang, Jincheng

doi:10.1007/s10623-021-00973-6

Cited by 1 publication

(2 citation statements)

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“…Non-commutative groups and rings have been used to propose a number of public-key cryptosystems and key exchange protocols [18][19][20]. According to [21][22][23], certain matrices properties, such as their determinant, eigenvalues, and Cayley-Hamilton theorem, can be exploited to create attacks against protocols that employ groups of invertible matrices over finite fields as their platform group. Such attacks reduce the DLP on GL n F q to the DLP over finite fields or a simple problem of factoring [23].…”

Section: Literature Reviewmentioning

confidence: 99%

“…According to [21][22][23], certain matrices properties, such as their determinant, eigenvalues, and Cayley-Hamilton theorem, can be exploited to create attacks against protocols that employ groups of invertible matrices over finite fields as their platform group. Such attacks reduce the DLP on GL n F q to the DLP over finite fields or a simple problem of factoring [23]. The semigroup of matrices over group ring: M k×k F q [S r ] under ordinary matrix multiplication operation [24] and the group of invertible matrices over group ring: GL n F q [S r ] [21] have been proposed as the platforms to prevent this reduction of DLP to the one over finite field.…”

Section: Literature Reviewmentioning

confidence: 99%

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Securing an Authenticated Privacy Preserving Protocol in a Group Signature Scheme Based on a Group Ring

Amir,

Othman,

Wong

2023

Mathematics

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Group signatures are a leading competing signature technique with a substantial amount of research. With group settings, group signatures provide user anonymity. Any group member with access to the group can generate a signature while remaining anonymous. The group manager, however, has the authority to expose and identify the signer if required. Since the privacy of the sender should be preserved, this is a conflict between privacy and accountability. Concerning high performance on security, we propose a novel, well-balanced security and privacy group signature scheme based on a general linear group over group ring. To the best of our knowledge, our work represents the first comprehensive framework for a group signature scheme that utilizes generic linear groups over group rings. We demonstrate that the competing security goals of message trustworthiness, privacy, and accountability are effectively resolved by our protocol. The results of the performance evaluation and simulation demonstrate that our protocol achieves strong security, system robustness, and high-performance efficiency, making it suitable for practical applications.

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