Abstract: This study focuses on protecting information against any broke attempts to known the data contents by transforming it into an unintelligible and secure format that allows information to be kept secret, so, we improved one of the most important methods used in the field of cryptography the asymmetric which uses a pair of keys that called RSA (Rivest-Shamir-Adleman) by multiplying the number of (public, private) keys to some extend “k” in the cryptosystem process and as well as how to apply proposal modified on set of digital gray images using MATLAB language, the practical results showed after comparative between traditional and modified algorithm, that (RSAM) gives more powerful security in the encryption process instead of conventional RSA and a high match ratio between original and decrypted images during data retrieval in the decryption process because it depends on computational hardness of the algorithm that based on “k” number of chosen (public, private) keys. Therefore, (RSAM) modified more confidential and safe for data privacy from unauthorized access attempts to detect or corrupt information.