Symmetric Encryption Scheme Based on Fuzzy Graph

The connection between the fuzzy set theory, graph theory and number theory for cryptographic algorithms is displayed here in this work. A fuzzy graph (FG) is employed to propose a new encryption scheme type symmetric (SES). In the proposed encryption algorithm, the ciphertext of the plaintext is sent to receiver as a FG. The triangular fuzzy membership (TFM) function is utilized to calculate the fuzzy values that are considered as the labels of a FG. The labels of the vertices \(\tilde{b}_{i}\) of FG are fuzzy values of the elements that form a subset of elements in a prime field Fp. The labels (weights) of the edges \(\tilde{a}_{i}\) of FG are also formed as a subset of long Fp. The usage of the fuzzy graph is proposed to increase the security of the SESs compared to other algorithms for encryption. Study case of the proposed fuzzy graphic encryption of symmetric type (FGSE) is discussed as a new computational result. The FGSE is considered as a suitable secure communication.