On representations of positive integers in the Fibonacci base

Edson, Marcia; Zamboni, Luca Q.

doi:10.1016/j.tcs.2004.06.025

Cited by 8 publications

(4 citation statements)

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“…If imposing the additional requirement that consecutive 1 are not allowed (viz. m i ≥ m i+1 + 2) and ε 1 cannot be '1' (F 1 = F 2 = 1, provided only F 2 = 1 admissible), then we obtain the canonical version of the definition [6][7][8][9]. Such a "canonical Zeckendorf representation" always exists and is unique [5].…”

Section: Preliminariesmentioning

confidence: 99%

Novel Stream Ciphering Algorithm for Big Data Images Using Zeckendorf Representation

Cai

2021

Wireless Communications and Mobile Computing

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Big data is a term used for very large data sets. Digital equipment produces vast amounts of images every day; the need for image encryption is increasingly pronounced, for example, to safeguard the privacy of the patients’ medical imaging data in cloud disk. There is an obvious contradiction between the security and privacy and the widespread use of big data. Nowadays, the most important engine to provide confidentiality is encryption. However, block ciphering is not suitable for the huge data in a real-time environment because of the strong correlation among pixels and high redundancy; stream ciphering is considered a lightweight solution for ciphering high-definition images (i.e., high data volume). For a stream cipher, since the encryption algorithm is deterministic, the only thing you can do is to make the key “look random.” This article proves that the probability that the digit 1 appears in the midsection of a Zeckendorf representation is constant, which can be utilized to generate the pseudorandom numbers. Then, a novel stream cipher key generator (ZPKG) is proposed to encrypt high-definition images that need transferring. The experimental results show that the proposed stream ciphering method, with the keystream of which satisfies Golomb’s randomness postulates, is faster than RC4 and LSFR with indistinguishable performance on hardware depletion, and the method is highly key sensitive and shows good resistance against noise attacks and statistical attacks.

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Section: Preliminariesmentioning

confidence: 99%