Non-Replicable Function-Based Multi-Level Random Dynamic Secret Key Algorithm

Based on the proof that, as an encryption function, the residual function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$y=(a x)_{\bmod m}$</tex> is a non-replicable function, this paper constructs multi-level encryption functions <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$y_{1}=\left(a_{1} x\right)_{\bmod m_{1}, \ldots, y_{n}=\left(a_{n} y_{n-1}\right)_{\bmod } m_{n} \text {. And based on }}$</tex> this the paper constructs the multi-level random dynamic secret key algorithm XM-1. XM-1 has three-fold safeguards. First, the encryption function is not replicable. Secondly, the secret keys and the number of secret keys are randomized. Thirdly, when the system does not run, there is no secret key. After slight changes, the four examples for constructing XM1given in this paper can be put into practical use.