Key exchange protocols over noncommutative rings. The case of

Climent, Joan‐Josep; Navarro, PedroR.; Tortosa, Leandro

doi:10.1080/00207160.2012.696105

Cited by 16 publications

(12 citation statements)

References 30 publications

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“…On the other hand, in [6] (see also [5,7]) the authors introduce a key exchange protocol over the noncommutative ring End(Z p × Z p 2 ) that fits with the previous protocol. In [11] the authors solve the DHDP problem using some invertible elements in End(Z p × Z p 2 ) resulting a cryptanalysis of that proposal.…”

Section: Alice Computesmentioning

confidence: 99%

Public key protocols over the ring $E_{p}^{(m)}$

Climent¹,

López-Ramos²

2016

AMC

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In this paper we use the nonrepresentable ring E (m) p to introduce public key cryptosystems in noncommutative settings and based on the Semigroup Action Problem and the Decomposition Problem respectively. IntroductionMost public-key cryptosystems are based on certain specific problems of number theory.One of these problems is the Integer Factorization Problem (IFP) over the ring Z n , being n the product of two large prime numbers; the well known cryptosystem RSA [22] is based in this problem. The second classical problem is the Discrete Logarithm Problem (DLP) over a finite field Z p , being p a large prime; the Diffie-Hellman key exchange protocol [9] and ElGamal protocol [10] are based on this problem. In general, we can say that their robustness depends on the computational difficulty of solving certain mathematical problems over finite commutative algebraic structures. Some efficient attacks based on the commutative property of these structures are well known: Quadratic Sieve, General Number Field Sieve, Pollard's rho algorithm, Index-Calculus, etc. (see, for example, [19,28], and the references within these books).This fact, together with the increase of the computational power of modern computers, has made these techniques become more and more insecure. As a result there exists an active field of research known as noncommutative algebraic cryptography (see, for example, [2,12,13,23,26]) aiming to develop and analyse new cryptosystems and key *

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Section: Alice Computesmentioning

confidence: 99%

Public key protocols over the ring $E_{p}^{(m)}$

Climent¹,

López-Ramos²

2016

AMC

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“…Subsequently, the use of non-commutative algebra in public key cryptography attracted a lot of attention. Several public key cryptosystems and key exchange protocols have been proposed using the non-commutative groups and rings [1,2,20]. As described in [4,11,12], certain properties of matrices like determinant, eigenvalues and Cayley-Hamilton theorem can be used to develop attacks against the protocol which uses group of invertible matrices over finite field as the platform group.…”

Section: Introductionmentioning

confidence: 99%

A key exchange protocol using matrices over group ring

Gupta

Pandey

Dubey

2019

Asian-European J. Math.

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The first published solution to key distribution problem is due to Diffie–Hellman, which allows two parties that have never communicated earlier, to jointly establish a shared secret key over an insecure channel. In this paper, we propose a new key exchange protocol in a non-commutative semigroup over group ring whose security relies on the hardness of Factorization with Discrete Logarithm Problem (FDLP). We have also provided its security and complexity analysis. We then propose a ElGamal cryptosystem based on FDLP using the group of invertible matrices over group rings.

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“…In Section 2 we recall some properties of the ring E (m) p . In Section 3 we introduce a multicast communication protocol initially defined over any noncommutative ring R, based on key exchanges developed by Climent, Navarro and Tortosa [8]. The implementation of the multicast protocol is performed over the ring E (m) p , due to its characteristics that make it safe to known attacks.…”

Section: Introductionmentioning

confidence: 99%

“…Using this ring and the arithmetic implemented over it, some key exchange protocols are presented in [8,9], using polynomials which coefficients are elements of the center of the ring. One of these protocols based on the noncommutative ring E p was cryptanalyzed by Kamal and Youssef [10].…”

Section: Introductionmentioning

confidence: 99%

Key agreement protocols for distributed secure multicast over the ringE^(m)_p

Climent

Ramos

Navarro

et al. 2013

WIT Transactions on Information and Communication Technologies

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Protocols for authenticated key exchange allow parties within an insecure network to establish a common session key which can then be used to secure their future communication. In this paper we introduce a protocol for distributed key agreement over a noncommutative ring with a large number of noninvertible elements. This protocol uses polynomials with coefficients in the center of the ring. We also present the necessary steps for recalculating the shared secret key when a new user joins the system, or when a user leaves the system. Secure communications, key exchange, noncommutative ring, multicast protocol

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Key exchange protocols over noncommutative rings. The case of

Cited by 16 publications

References 30 publications

Public key protocols over the ring $E_{p}^{(m)}$

Public key protocols over the ring $E_{p}^{(m)}$

A key exchange protocol using matrices over group ring

Key agreement protocols for distributed secure multicast over the ringE^(m)_p

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Key exchange protocols over noncommutative rings. The case of

Cited by 16 publications

References 30 publications

Public key protocols over the ring $E_{p}^{(m)}$

Public key protocols over the ring $E_{p}^{(m)}$

A key exchange protocol using matrices over group ring

Key agreement protocols for distributed secure multicast over the ringE(m)p

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Product

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Key agreement protocols for distributed secure multicast over the ringE^(m)_p