Image Encryption Scheme Based on a Truncated Baker Transformation

Kenji YANO  Kiyoshi TANAKA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E85-A    No.9    pp.2025-2035
Publication Date: 2002/09/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
chaos,  truncated Baker transformation,  image encryption,  Peano scanning order,  

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In this paper, we focus on an image encryption scheme based on a truncated Baker transformation. The truncated Baker transformation globally preserves the original dynamics of Baker transformation but incorporates a random local rotation operator between two neighbor elements in the mapping domain in order to keep a finite precision. It generates binary sequences (the dynamics of elements) which have statistically good features on ergodicity, mixing and chaotic properties. The image encryption scheme extended from the truncated Baker transformation efficiently shuffles the input gray level image satisfying fundamental conditions on confusion and diffusion required for image encryption schemes. However, this scheme uses many binary sequences and thus needs to keep a large volume of secret keys. In order to solve this problem we introduce Peano space-filling curve in this scheme, which remarkably reduce the key size and mapping iterations without deteriorating good shuffling properties attained by this scheme.