Efficient Chaotic Encryption Scheme with OFB Mode

Data confidentiality is mandatory during transmission or when storing sensitive information, especially in financial, medical and military applications. In this context, several cipher solutions and techniques have been presented in the literature. However, existing solutions are mainly based on static structures, where the confusion and diffusion primitives are fixed and independent of the secret key. In this article, we propose a new block cipher scheme that is based on the Substitution Permutation Networks (SPN). The proposed cipher consists of three operations: round-key addition, substitution, and bits' permutation. Moreover, the substitution operation is applied at the byte level and it is based on a dynamically generated S-box, while the diffusion primitives are applied at the bit level using a dynamically generated P-box. Such key-dependent design ensures better cryptographic strength and system performance when compared, for instance, to DES, 3DES, RC5, and PRESENT schemes, among others, due to its key expansion algorithm. Thorough analysis show that the proposed scheme exhibits a high degree of randomness, key and plain-text sensitivity, and it satisfies the avalanche effect. From a theoretical perspective, we have formulated the Output Feedback mode of operation as a discrete dynamical system on a topological space. We prove that the dynamics of this system (in terms of sensitivity to the initial vector, etc.) are directly related to the strong connectivity of a graph. By doing so, we are able to characterize the conditions under which this mode evolves chaotically, as defined in Devaney's theory. In particular, such theoretical investigations allow us to link the avalanche effect and key sensitivity of the cipher with the sensitivity of the whole process, that is, with the mode of operation.