Examination and implementation of the fast method for computing the order of elliptic curve

Gorbenko, I.D.; Hanzia, Roman

doi:10.15587/1729-4061.2017.95194

Cited by 20 publications

(1 citation statement)

References 7 publications

(48 reference statements)

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“…The Chinese remainder theorem states that if we know the remainder of the Euclidean division of an integer n by several integers, we can uniquely determine the remainder of the division of n by the product of these integers, provided that the divisors are prime to each other [32][33][34][35]. CRT algorithm is used to convert from RNS to the binary system [36][37][38].…”

Section: Chinese Remainder Theorem (Crt)mentioning

confidence: 99%

An efficient image cryptosystem based on the residue number system and hybrid chaotic maps

Kari¹,

Ghomian

2023

Preprint

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This paper presents a new method for encrypting gray-scale digital images. The proposed method uses a combination of the residue number system and chaotic maps to avoid the complexities of high-dimensional chaotic maps and improve the security of encryption and processing speed. In this method, the image pixel coordinates confusion operation is performed by Arnold's cat map, and the pixel content diffusion step is performed in two phases. In the first phase, the contents of the image pixels are converted to the introduced {(r-1)a, rb, (r + 1)c} residue number system and stored in a matrix. At the same time, a chaotic system produces a combination of Sinusoidal and Logistic maps of chaotic sequences, and after quantization, they are converted into the introduced residue number system and stored in another matrix of the same size. In the second phase of diffusion, XOR operation is performed between these two matrices. The implementation results show that the use of the residue number system, in addition to improving the evaluation parameters, improves the processing time, and the average processing time for encryption is 0.15 seconds. Also, the uniform histogram, the entropy of about 8, and the correlation coefficient close to 0 of the encrypted images all demonstrate the high security of the proposed method.

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