The Period of 3-D Random Matrix Scrambling Transformation and Its Applications
Zehui Wang · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2008
For implementing the encryption/decryption and information hiding for digital multimedia,and aiming to generate enough large cipher key space,the accurate period of high dimension random matrix scrambling transformation is studied with the help of number theory and algebraic theory.An accurate expression and an upper bound estimation for the period T(A,N) of a 3-D random integer matrix scrambling transformation under any modular N is presented.The efficient algorithm for computing the period is constructed.It is proved that the algorithm needs only O(log2N)2 times multiplications modulo N for determining the period T(A,N).Many practical demonstration examples verified the results.This approach can be used to construct new efficient cryptosystems for digital multimedia encryption/decryption.