A New Kind of Digital Signature Scheme Using Golden Matrices Based on Factoring Problem

Bani-Ahmad, Feras; Shatnawi, Mohd Taib; Tahat, Nedal; Shatnawi, Safaa

doi:10.12732/ijpam.v107i1.5

Cited by 5 publications

(3 citation statements)

References 5 publications

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“…In a number of papers [7,10,11] and books [8,12] Stakhov developed the so-called "golden cryptography", a system of encryption based on utilizing matrices with entries being consecutive Fibonacci numbers with fast encryption/decryption and nice error-correction properties. It was applied to creating digital signatures [1], and somewhat similar techniques are used for image encryption and scrambling [3]. However, the golden cryptography and its generalizations are vulnerable to the chosen plaintext attacks, which make it insecure [6,14].…”

Section: Introductionmentioning

confidence: 99%

From golden to unimodular cryptography

Koshkin

Styers

2017

Chaos, Solitons & Fractals

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We introduce a natural generalization of the golden cryptography, which uses general unimodular matrices in place of the traditional Q matrices, and prove that it preserves the original error correction properties of the encryption. Moreover, the additional parameters involved in generating the coding matrices make this unimodular cryptography resilient to the chosen plaintext attacks that worked against the golden cryptography. Finally, we show that even the golden cryptography is generally unable to correct double errors in the same row of the ciphertext matrix, and offer an additional check number which, if transmitted, allows for the correction.

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Section: Introductionmentioning

confidence: 99%

From golden to unimodular cryptography

Koshkin

Styers

2017

Chaos, Solitons & Fractals

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“…Golden cryptography, as originally proposed by Stakhov [21,22], is a type of matrix encryption where the matrices are 2 × 2 and their entries are consecutive terms of the Fibonacci sequence. It has attractive error detection and correction properties, and was applied to creating digital signatures [4], and, with some modifications, to image encryption and scrambling [15]. However, it is vulnerable to brute force and chosen plaintext attacks [19,24] due to a small number of parameters in the encryption key that are relatively easy to guess or back engineer.…”

Section: Introductionmentioning

confidence: 99%

Linear recurrent cryptography: golden-like cryptography for higher order linear recurrences

Koshkin,

Rodriguez

2022

Preprint

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We develop matrix cryptography based on linear recurrent sequences of any order that allows securing encryption against brute force and chosen plaintext attacks. In particular, we solve the problem of generalizing error detection and correction algorithms of golden cryptography previously known only for recurrences of a special form. They are based on proving the checking relations (inequalities satisfied by the ciphertext) under the condition that the analog of the golden Q-matrix has the strong Perron-Frobenius property. These algorithms are proved to be especially efficient when the characteristic polynomial of the recurrence is a Pisot polynomial. Finally, we outline algorithms for generating recurrences that satisfy our conditions.

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“…It is observed that the size of keys and storage space can be reduced by representing the plain text message as a matrix [9], [10], [11] without compromising the security. In [12] Bani et.al proposed a new kind of digital signature scheme using golden matrices which is a fast signature and can be used for protection of digital signals. Recently M. Basu et al [13] introduced a new coding theory called Tribonacci coding theory based on Tribonacci matrices that are the generalization of Fibonacci numbers.…”

Section: Introductionmentioning

confidence: 99%

A New Digital Signature Scheme Using Tribonacci Matrices

Sanghi

2020

IJCIT

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Achieving security is the most important goal for any digital signature scheme. The security of RSA, the most widely used signature is based on the difficulty of factoring of large integers. The minimum key size required for RSA according to current technology is 1024 bits which can be increased with the advancement in technology. Representation of message in the form of matrix can reduce the key size and use of Tribonacci matrices can double the security of RSA. Recently M.Basu et.al introduced a new coding theorycalled Tribonacci coding theory based onTribonacci numbers, that are the generalization ofthe Fibonacci numbers. In this paper we present anew and efficient digital signature scheme usingTribonacci matrices and factoring.

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A New Kind of Digital Signature Scheme Using Golden Matrices Based on Factoring Problem

Cited by 5 publications

References 5 publications

From golden to unimodular cryptography

From golden to unimodular cryptography

Linear recurrent cryptography: golden-like cryptography for higher order linear recurrences

A New Digital Signature Scheme Using Tribonacci Matrices

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