Encryption Schemes with Hyper-Complex Number Systems and Their Hardware-Oriented Implementation

Quaternion Encryption Scheme (QES) is shown to be susceptible to the Known Plaintext-Ciphertext Attack (KPCA) due to improper choice of frame size and the procedure of secret quaternion updating. In this chapter, the authors propose a modification of the QES (M-QES) that is resistant to the KPCA. The M-QES is based on adjusting the frame size and the quaternion update procedure. An approach for effective hardware implementation of the proposed algorithm, HW-QES, is discussed. The HW-QES uses addition and shift operations. Extension of quaternion approach to another hyper-complex number systems, octonions, is used for designing a new hardware-oriented encryption algorithm, HW-OES. Experimental results show that the proposed M-QES and HW-QES are six-eight times more effective in the encryption quality of signals than the original QES. Additionally, M-QES and HW-OES are shown to be significantly more effective in the encryption quality of images than the original QES and well-known AES. The results show that the performance of the HW-QES is only 10% worse than that of QES.