This paper proves invariable coefficient rule of the image in discrete cosine and wavelet transformation when it is scrambled in space domain. Based on the constructed composite chaotic iterative dynamic system, whose invariant distribution density is one, and in order to initialize composite chaotic iterative dynamic system, it puts forward two constructed functions using image scramble constant as input parameter. A fragile and adaptive image scrambling algorithm and two new scrambling evaluative parameters called similitude degree and anti-tamper radius are given. Experiments show that the ...