An invertible chaotic 3D map based image ecnryption approach and its optimized algorithm are proposed utilizing the stretch and fold mechanism of chaos. A gray-level image is firstly depicted as a 3D matrix. Then the 3D matrix is mapped to a 2D image matrix according to the proposed algorithm. Stretch and fold maps are used to permute pixel positions of the 2D matrix. The stretch process is to transform the 2D image matrix to an array

while the fold process is to fold the array to another 2D image matrix which is the same size as the original 2D matrix. At last

the permuted 2D matrix is mapped back to a 3D matrix

cipher image is achieved. This proposed approach is invertible

it could be used for image encryption and decryption. The encryption and decryption algorithms are formulated. Since image has large data quality

if the deduced formulas are used for image encryption and decryption

there will be large amount of calculation and long encryption and decryption time. In order to solve this problem

an optimized algorithm is proposed. Image encryption and decryption experiments were did and key sensitivity

correlation coefficients of two adjacent pixels and the time used for image encryption and decryption are tested. The results show that proposed image encryption approach realize pixel permutation and substitution at the same time via one iteration map

it change the histogram information of the plain image

enhance the capability of resisting statistic attack

have big key space. The proposed optimized algorithm obviously increase image encryption speed

it is faster than using the deduced formulas about 3 to 4 times.