2020
DOI: 10.3390/e22040454
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Image Encryption Using Elliptic Curves and Rossby/Drift Wave Triads

Abstract: We propose an image encryption scheme based on quasi-resonant Rossby/drift wave triads (related to elliptic surfaces) and Mordell elliptic curves (MECs). By defining a total order on quasi-resonant triads, at a first stage we construct quasi-resonant triads using auxiliary parameters of elliptic surfaces in order to generate pseudo-random numbers. At a second stage, we employ an MEC to construct a dynamic substitution box (S-box) for the plain image. The generated pseudo-random numbers and S-box are used to pr… Show more

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Cited by 18 publications
(18 citation statements)
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“…It is worth mentioning that for the RSA algorithm to achieve the same level of security as the ECC technique, it basically requires an increased key length. Although RSA introduces simple computations, the ECC depends on DLP with a lesser key length [37]. Table 2 summarizes the comparative results between RSA, OSS-ECC, and the modified OSS-ECC in signature computation time with respect to key length, which achieved the same security level for all compared schemes.…”
Section: Resultsmentioning
confidence: 96%
See 1 more Smart Citation
“…It is worth mentioning that for the RSA algorithm to achieve the same level of security as the ECC technique, it basically requires an increased key length. Although RSA introduces simple computations, the ECC depends on DLP with a lesser key length [37]. Table 2 summarizes the comparative results between RSA, OSS-ECC, and the modified OSS-ECC in signature computation time with respect to key length, which achieved the same security level for all compared schemes.…”
Section: Resultsmentioning
confidence: 96%
“…Their key-dependent S-box was constructed with the logistic map. Guo et al [37] presented an extended method for designing S-Box based on three-dimensional chaotic Baker maps. This depends on obtaining strong 8 × 8 S-boxes.…”
Section: Substitution-box (S-box) Constructionmentioning
confidence: 99%
“…Related work: Like chaotic maps, elliptic curves (ECs) are highly sensitive to the initial parameters, and a number of EC-based algorithms have been developed for cryptographic applications [9,[35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Zhang and Wang [40] used the group law for the generation of a public key and encrypted digital images by combining a chaotic system and elliptic curve cryptography (ECC).…”
Section: Introductionmentioning
confidence: 99%
“…Murillo-Escobar et al [37] proposed a new text encryption scheme based on a logistic map. Similarly, elliptic curves (ECs) received great attention in the field of cryptography for image encryption [43][44][45][46][47], text encryption [48][49][50][51][52][53] and signcryption [54][55][56] due to comparable security against modern cryptanalysis with low key size. Sunneetha et al [48] proposed a secure algorithm using elliptic curves and algebraic operations to transmit messages.…”
Section: Introductionmentioning
confidence: 99%