Cryptosystem based on a key function of a real variable

Abstract

Using the function of a real variable in cryptosystems as a key allows you to increase its cryptographic strength, because it is more difficult to pick up such key. Therefore, the development of such systems is relevant. A cryptosystem with a symmetric key is offered. This key is some function of a real variable that satisfies some restrictions. It can be either continuous or discrete.
 The transmitting and receiving parties select the key-function, the first transmitted character or the first transmitted value for the analog message, the function area of the key function, and the step of changing the function argument. A Disproportion over first-order derivative is used to encrypt an analog message.
 The Cauchy problem is solving for decrypting this message. Discrete messages are encrypted using the first-order disproportionality integral function. Decryption is performed by the inverse transformation of the formula for integral disproportion.
 Algorithms for encrypting and decrypting messages are presented. The ability to encrypt and decrypt text information, 2D graphic images, as well as analog messages are shown. The examples show the complexity to pick up the key function and the cryptographic strength of the proposed cryptosystem.
 A cryptosystem, in which the function of a real variable is used as a key and as well as disproportion functions are used, is suitable for encryption of both discrete and continuous messages. To “crack” such a system, it is required to pick up the form of the key function and to find the values of its parameters with very high accuracy. That is, the system has high cryptographic strength.