Abstract: Based on the idea of multiplication inverse of Euclid algorithm, two easy construction methods for generalized cat map were presented. One is based on the Fibonacci series and the other is based on the Dirichlet series. Moreover,one construction method was presented combined with these two series. Simulation experiments show that the period of generalized cat map is alterable and greater compared with that of cat map, thus they have better scrambling effect and also make them much securer than cat map and Fibonacci transform. In practice they can find great value in practice in image information hiding for storage and transmission and provide a much solider theoretical foundation for image scrambling.

Key words: Euclid algorithm,Image scrambling,Generalized cat map,Dirichlet series,Fibonacci series