Public key exchange using matrices over group rings

Kahrobaei, Delaram; Koupparis, Charalambos; Shpilrain, Vladimir

doi:10.1515/gcc-2013-0007

Cited by 67 publications

(52 citation statements)

References 5 publications

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“…We propose a polynomial time quantum algorithm for solving the discrete logarithm problem in matrices over finite group rings. The hardness of this problem was recently employed in the design of a key-exchange protocol proposed by D. Kahrobaei, C. Koupparis, and V. Shpilrain [4]. Our result implies that the Kahrobaei et al protocol does not belong to the realm of post-quantum cryptography.…”

mentioning

confidence: 72%

“…2: Bob chooses a random secret b with 1 ≤ b ≤ p − 2 and sends g b mod p to Alice. 3: Alice receives g b and computes the shared key as K = (g b ) a mod p. 4: Bob receives g a and computes the shared key as K = (g a ) b mod p.…”

Section: One-time Setupmentioning

confidence: 99%

“…That proposal was cryptanalyzed by Meneses and Wu in [8] who showed that there exists a probabilistic polynomial time reduction of DLP in GL n (F p s ) to DLP in some small extension field of F p s , proving that the proposal brings nothing new to the field. More recently, D. Kahrobaei, C. Koupparis, and V. Shpilrain in [4] considered yet another variation of the Diffie-Hellman key-exchange protocol which uses the ring of 3 × 3 matrices over a group-ring F 7 [S 5 ]. The authors claim that the new scheme can withstand quantum algorithm attacks and provide some supporting arguments.…”

Section: One-time Setupmentioning

confidence: 99%

“…The protocol proposed by Kahrobaei et al [4] works exactly the same way as the original Diffie-Hellman. We describe it here just to fix the notation and parameter values:…”

Section: Group Rings and Kahrobaei Et Al Protocolmentioning

confidence: 99%

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Quantum algorithm for discrete logarithm problem for matrices over finite group rings

Myasnikov

Ushakov

2014

Groups Complexity Cryptology

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Abstract. We propose a polynomial time quantum algorithm for solving the discrete logarithm problem in matrices over finite group rings. The hardness of this problem was recently employed in the design of a key-exchange protocol proposed by D. Kahrobaei, C. Koupparis, and V. Shpilrain [4]. Our result implies that the Kahrobaei et al. protocol does not belong to the realm of post-quantum cryptography.

show abstract

mentioning

confidence: 72%

Section: One-time Setupmentioning

confidence: 99%

Section: One-time Setupmentioning

confidence: 99%

“…The protocol proposed by Kahrobaei et al [4] works exactly the same way as the original Diffie-Hellman. We describe it here just to fix the notation and parameter values:…”

Section: Group Rings and Kahrobaei Et Al Protocolmentioning

confidence: 99%

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Quantum algorithm for discrete logarithm problem for matrices over finite group rings

Myasnikov

Ushakov

2014

Groups Complexity Cryptology

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“…In 2016, using semidirect product of two groups, Habeeb et al [7] proposed a key exchange protocol (the HKKS protocol) based on the work of [8,9]. Unlike all the operating principles of the existing Diffie-Hellmanlike protocols, its basic passive security is based on a stronger computational group-theoretic assumption than the current assumptions of hardness of discrete logarithm problems.…”

Section: Introductionmentioning

confidence: 99%

An Authenticated Key Agreement Scheme Based on Cyclic Automorphism Subgroups of Random Orders

Zhang

2017

ITM Web Conf.

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Abstract:Group-based cryptography is viewed as a modern cryptographic candidate solution to blocking quantum computer attacks, and key exchange protocols on the Internet are one of the primitives to ensure the security of communication. In 2016 Habeeb et al proposed a "textbook" key exchange protocol based on the semidirect product of two groups, which is insecure for use in real-world applications. In this paper, after discarding the unnecessary disguising notion of semidirect product in the protocol, we establish a simplified yet enhanced authenticated key agreement scheme based on cyclic automorphism subgroups of random orders by making hybrid use of certificates and symmetric-key encryption as challenge-and-responses in the public-key setting. Its passive security is formally analyzed, which is relative to the cryptographic hardness assumption of a computational number-theoretic problem. Cryptanalysis of this scheme shows that it is secure against the intruder-in-the-middle attack even in the worst case of compromising the signatures, and provides explicit key confirmation to both parties.

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Verifiable Chebyshev maps‐based chaotic encryption schemes with outsourcing computations in the cloud/fog scenarios

Wang

et al. 2018

Concurrency and Computation

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SummaryBased on cloud servers' powerful storage and computing resources, users can store mass encrypted data in the cloud and outsource complex encryption computations to the cloud servers. Since cloud servers cannot be completely trusted, then data privacy and integrity are concerned about hot issues. We focus on the following problems in outsourced encryptions: how to protect the data privacy and how to check the integrity of data and the correctness of cloud server's outsourcing computations. In this paper, we at first propose a verifiable chaotic encryption based on Chebyshev polynomials. The scheme supports verifiable function for data integrity. To further improve the efficiency of the scheme, a corresponding outsourced encryption scheme is constructed, where the heavy overhead evaluations of Chebyshev polynomials are transferred from the user side to the cloud server. The outsourced encryption also provides the checkability for data integrity and correctness of cloud computations. The scheme is suitable for mobile users with limited computing resources. Moreover, the newly proposed scheme no longer depends upon the simple heuristic analysis. It achieves the indistinguishability under chosen‐ciphertext attacks (IND‐CCA) in the standard model based on the Chebyshev‐based Decisional Diffie‐Hellman (CDDH) assumption. Thus, we answer a long‐term open problem for building a chaotic encryption scheme with provable security in the sense of the IND‐CCA.

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Public key exchange using matrices over group rings

Cited by 67 publications

References 5 publications

Quantum algorithm for discrete logarithm problem for matrices over finite group rings

Quantum algorithm for discrete logarithm problem for matrices over finite group rings

An Authenticated Key Agreement Scheme Based on Cyclic Automorphism Subgroups of Random Orders

Verifiable Chebyshev maps‐based chaotic encryption schemes with outsourcing computations in the cloud/fog scenarios

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