Improvement of Rhouma's attacks on Gao algorithm

After comprehensive analysis of attacks proposed by Rhouma on Gao algorithm, limitations of the attacks are introduced — Rhouma's chosen plaintext attack (CPA) and chosen ciphertext attack   (CCA) aren't suitable for breaking Gao algorithm when the size of ciphered image is in excess of 255×255255×255. Then, an extended version of Rhouma's CPA and a new CCA are proposed to deal with ciphered image of arbitrary size M×NM×N; by constructing (⌈M/255⌉+⌈N/255⌉)+1(⌈M/255⌉+⌈N/255⌉)+1 images. The validities of the two new attacks are proved by Proposition 1 and Proposition 2 respectively. Finally, experiments show the validities of our analysis and attacks.