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Quaternion encryption methods for multimedia transmission, a survey of existing approaches

Dzwonkowski M., Rykaczewski R.

Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne

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2016

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nr 7

668--671

EN

In this paper we review quaternion encryption methods for multimedia transmission. We explain their weak and strong properties as well as suggest possible modifications. Our main focus is an algorithm QFC presented in paper by Dzwonkowski et al. (2015). All encryption methods, presented in this paper, use special properties of quaternions to perform rotations of data sequences in 3D space. Each method uses a common key generation algorithm (to form an infinite key space), as well as a modular arithmetic for operations with quaternions. A computer-based analysis has been carried out for all encryption methods. The obtained results are discussed at the end of this paper.

PL

Artykuł jest poswięcony analizie znanych metod szyfrowania kwaternionowego dla zabezpieczania danych multimedialnych. Skupiono się na wyeksponowaniu ich słabych i silnych stron oraz zaproponowaniu możliwych modyfikacji. Tematem przewodnim artykułu jest analiza algorytmu QFC zaproponowanego przez autorów w pracy Dzwonkowski i in. (2015). Omawiane w tym artykule metody szyfrowania wykorzystują właściwości ciała kwaternionów do przeprowadzania rotacji wektorów danych w przestrzeni trójwymiarowej. Wszystkie metody wykorzystują ten sam algorytm generacji kluczy oraz arytmetykę modularną dla operacji kwaternionowych. Opisywane metody szyfrowania kwaternionowego zbadano za pomocą symulacji komputerowej, a otrzymane wyniki przeanalizowano pod kątem odporności na ataki kryptoanalityczne.

2

Quaternion Feistel Cipher with an Infinite Key Space Based on Quaternion Julia Sets

Dzwonkowski M., Rykaczewski R.

Journal of Telecommunications and Information Technology

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2015

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nr 4

15--21

EN

In this paper Quaternion Feistel Cipher (QFC) with an infinite key space based on quaternion Julia sets is proposed. The basic structure of the algorithm is based on the scheme proposed in 2012 by Sastry and Kumar. The proposed algorithm uses special properties of quaternions to perform rotations of data sequences in 3D space for each of the cipher rounds. It also uses Julia sets to form an infinite key space. The plaintext is divided into two square matrices of equal size and written using Lipschitz quaternions. A modular arithmetic was implemented for operations with quaternions. A computer-based analysis has been carried out and obtained results are shown at the end of this paper.

3

Digital Fingerprinting Based on Quaternion Encryption Scheme for Gray-Tone Images

Czaplewski B., Dzwonkowski M., Rykaczewski R.

Journal of Telecommunications and Information Technology

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2014

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nr 2

3--11

EN

In this paper a new idea of digital images fingerprinting is proposed. The method is based on quaternion encryption in the Cipher Block Chaining (CBC) mode. Quaternions are hyper-complex numbers of rank 4 and thus often applied to mechanics in three-dimensional space. The encryption algorithm described in the paper is designed for graytone images but can easily be adopted for color ones. For the encryption purpose, the algorithm uses the rotation of data vectors presented as quaternions in a three-dimensional space around another quaternion (key). On the receiver's side, a small amount of unnoticeable by human eye errors occurs in the decrypted images. These errors are used as a user's digital figerprint for the purpose of traitor tracing in case of copyright violation. A computer-based simulation was performed to scrutinize the potential presented quaternion encryption scheme for the implementation of digital fingerprinting. The obtained results are shown at the end of this paper.