With the accelerated advancement in network technologies, an increasing number of images and videos with exclusive and secret information are produced, diffused and saved in our modern life. These images are in peril of numerous attacks so that the security issue becomes progressively significant in data storage and transmission. Image encryption is an effective way to avoid the threats. The approaches of image encryption are generally divided into two groups based on spatial and frequency domains, respectively. In this thesis, our main contributions also are twofold. First, we propose two encryption methods based on the bitplane decomposition and edge map techniques, respectively, in the spatial domain: image encryption using binary bitplane (DecomCrypt) and an edge map-based medical image encryption (EMMIE). These two methods are readily implemented in hardware and suitable for encrypting bulk data, e.g. medical images. Besides, they are data-lossless methods with high-security levels. The other contribution is a multi-stage image encryption algorithm (MSIEA) in the frequency domain. In this encryption method, we proposed a modeling scheme of the fast Fourier transform (FFT) to reduce both the multiplicative complexity and the total number of operations and to decompose the discrete Fourier transform (DFT) matrix recursively into a set of sparse matrices. Integrating different orthogonal transforms (e.g. the Hadamard, modified Haar, and hybrid transforms) the proposed scheme made an application to image encryption with fewer computation operations and a higher security level than most state-of-the-art methods. Particularly, the main achievements of this thesis are elaborated as follows.1. A flexible image encryption method, called DecomCrypt, is based on bitplane decomposition in the spatial domain. Users have the flexibility to choose (1) any existing or newly generated image as the source image; (2) any decom-position method for generating the bitplanes; (3) any decomposed bitplane as security key bitplane; and (4) any scrambling method for bit-level permutation. As an example, we also propose a bit-level scrambling algorithm to change bit positions. DecomCrypt has a huge key space because any image could act as the source image and any image scrambling method could be used for changing bit positions. Simulations and security analysis have demonstrated that Decom-Crypt is highly sensitive to the security key, which exhibits excellent encryption performance for protecting different types of images and outperforms state-of-art algorithms in terms of security and encryption performance. DecomCrypt also has potential applications in the area of multimedia communications. 2. A medical image encryption technique, named EMMIE, applies edge map technique in the spatial domain. The algorithm is composed of three parts: bit-plane decomposition, generator of random sequence, and permutation. It offers users the following flexibilities: (1) any type of images can be used as the source image; (2) different edge maps can be generated by various edge detectors and thresholds; (3) selection of appropriate bit-plane decomposition method is flexible; and (4) many permutation methods can be cascaded with the proposed algorithm. Since the proposed algorithm possesses a significantly large key space and strong key sensitive it is able to protect different types of medical images. Furthermore, it has a wider applicability than other methods for fuzzy edge map-s. The histograms of the cipher-images are approximately flat even with blurry edge maps. It verifies that EMMIE possesses a strong robustness for fuzzy edge maps according to the simulation results. The analysis of security demonstrates that EMMIE is a secure algorithm. The keys of EMMIE, including the source image, edge detector, and the parameters of a scrambling method, are significantly large to defend the Bruce-force attack. To further evaluates the security level, EMMIE is compared with other state-of-the-art methods. Results have verified that EMMIE possesses a higher pixel correlation, stronger key sensitivity and error robustness, and a better performance against the differential attack with less time cost. 3. In the frequency domain, a multi-stage image encryption algorithm, named M-SIEA, is built on a new modeling scheme of the fast Fourier transform (FFT) to decompose the discrete Fourier transform (DFT) matrix recursively into a set of sparse matrices. We choose the Hadamard, modified Haar, and Hybrid (Hadamard-Haar) transforms as examples to show its effectiveness. The pro-posed model significantly reduces the computation complexity and shows better performance than several state-of-the-art FFT methods. Experimental comparisons and security analysis have demonstrated the proposed algorithm has good encryption performance and is able to protect different types of images with multiple security levels in the frequency domain.