Encrypting Images Using the Sum of Functions of a Real Variable

A combined cryptosystem with symmetric keys for encrypting messages is proposed. Its unique feature is the use of functions of a real variable as keys instead of natural numbers. Eight key functions correspond to the eight binary digits in the ASCII character code, with each binary digit assigned a specific key function. The cipher for each character is represented as a one-dimensional array of real numbers. The elements of the array are generated by summing selected key functions, where the amplitudes are chosen randomly. Only the key functions corresponding to binary digit “1” in the ASCII code of the character being encrypted are summed. Each array is subsequently encrypted by calculating the integral disproportion function using either a new key function or one employed in the initial stage. Decryption is similarly performed in two stages. Examples are provided to illustrate the robustness of this cryptographic system.