Optical encryption of hyperspectral images using improved binary tree structure and phase-truncated discrete multiple-parameter fractional Fourier transform

Abstract

We present an optical encryption scheme for hyperspectral images using an improved binary tree structure (IBTS) and phase-truncated discrete multiple-parameter fractional Fourier transform (PTdmpFrFT). In the IBTS, the encryption modules based on the phase-truncated fractional Fourier transform represented the branch nodes, while the hyperspectral bands of the plain images were considered as leaf nodes. All pairs of bands were encoded into intermediate data using the IBTS, with subsequent encryption into asymmetric ciphertexts using the PTdmpFrFT. The proposed approach generated different pairs of bands with different secret keys, and encryption and decryption paths. Compared with state-of-the-art optical hyperspectral encryption methods, our approach not only achieved superior encryption security but also reduced the computation and storage requirements of the encrypted data. The original hyperspectral image information could be successfully decrypted only when using all the correct keys. Numerical simulations were performed to verify the performance of the proposed method.

Key Validity Using the Multiple-parameter Fractional Fourier Transform for Image Encryption

“…In the encryption process, multiple keys are used to expand the key space of the system and thus have better security. Since then, the MPFRFT has become an important means to protect information security, and many research results have been proposed [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The MPFRFT is an extended definition of multifractional Fourier transform [17].…”

“…One is to use the MPFRFT combined with other encryption methods to ensure security [2][3][4][5][6][7]. For example, its combination with chaos is currently the most used encryption strategy [2][3][4][5], and its combination with other scrambling techniques [6,7], and so on. The second is the improvement of the algorithm.…”

Key Validity Using the Multiple-Parameter Fractional Fourier Transform for Image Encryption

“…In the encryption process, multiple keys are used to expand the key space of the system and thus have better security. Since then, the MPFRFT has become an important means to protect information security, and many research results have been proposed [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The MPFRFT is an extended definition of multifractional Fourier transform [19].…”

“…Compared with previous encryption schemes [19,20], the MPFRFT not only uses the period and the transformation order as the keys, but also introduces two vector parameters, and vector parameters increase with the increase of the period, so it has better security. The existing encryption schemes mainly focus on two aspects: One is to use the MPFRFT combined with other encryption methods to ensure security [4][5][6][7][8][9]. For example, its combination with chaos is currently the most used encryption strategy [4][5][6][7], and its combination with other scrambling techniques [8,9], and so on.…”

“…The existing encryption schemes mainly focus on two aspects: One is to use the MPFRFT combined with other encryption methods to ensure security [4][5][6][7][8][9]. For example, its combination with chaos is currently the most used encryption strategy [4][5][6][7], and its combination with other scrambling techniques [8,9], and so on. The second is the improvement of the algorithm.…”