Public-key cryptography can be claimed as the greatest and an excellent revolution in the field of cryptography. A public-key cryptosystem is used for both confidentiality and authentication. One such public-key cryptosystem is the RSA cryptosystem. In this paper, a modified and an enhanced scheme based on RSA public-key cryptosystem is developed. The proposed algorithm makes use of four large prime numbers which increases the complexity of the system as compared to traditional RSA algorithm which is based on only two large prime numbers. In the proposed Enhanced and Secured RSA Key Generation Scheme (ESRKGS), the public component n is the product of two large prime numbers but the values of Encryption (E) and Decryption (D) keys are based on the product of four large prime numbers (N) making the system highly secured. With the existing factorization techniques, it is possible only to find the primes p and q. The knowledge of n alone is not sufficient to find E and D as they are based on N. The time required for cryptanalysis of ESRKGS is higher than traditional RSA cryptosystem. Thus the system is highly secure and not easily breakable. A comparison is done between the traditional RSA scheme, a recent RSA modified scheme and our scheme to show that the proposed technique is efficient.