ABSTRACT
The rapid growth of cybersecurity challenges demands faster and stronger cryptographic algorithms for text and image encryption. This study introduces a new encryption algorithm based on the concept of the Fermat theorem and the use of trigonometric functions and transformations and the current cryptographic tools. The proposed approach will improve the security of data, as it is a more robust approach to saving sensitive information that combines the characteristics of transcendental number and trigonometric transformations. A prime number that is congruent to one, modulo four defines two secret keys which Fermat has established in his Theorem. The keys are then applied during the trigonometric transformation phases of encryption process. The protocol uses the decimal representation of a transcendental number to encode the plaintext characters to unique numerical values adding resistance to frequency and brute force attacks. Tangent and arctangent functions are trigonometric transformations that are used in both encrypting and decrypting the messages, which transform the integers into floating point numbers, and bring great non-linearity in the communication medium. The characteristics of trigonometric function and transcendental number lay a mathematically sound system guaranteeing a high entropy and accurate reversibility. Experimental verification spells out that the decryption protocols recover the original secret message with perfect fidelity, which makes the accuracy and reliability of the proposed method.
