RSA cryptography is presently used in a wide variety of products (TCP/IP, MIME, WAN, TELNET etc), platform (Apple, Sun, Novel, and Microsoft) around the world computer network for securely communication and transformation. Security strength of RSA Cryptography is an enormous mathematical integer factorization problem. This book introduced very significant integer factoring algorithms such as trial division, ρ- method ECM, and NFS and effort to factor RSA-150 composite number ‘n’ of 512 bits by using NFS. It is found that the RSA-150 may be believed to safe from the intruder. However, this system is slow for large volume of data. Essentially the computation of encryption and decryption process required high memory space and execution time. Java ‘BigInteger’ class is introduced in this book and successfully applied to overcome this shortcoming. Furthermore the implementation of RSA-1024 Cryptographic system by using Java RMI over a network is discussed. Wherein, RSA modulus ‘n’ of size 1024 bits is used. This implementation is extremely supportive when readers are eager to use RSA algorithm in their applications. Finally recent research scope of RSA cryptography is discussed as well.