This research work emerged as a new concept to provide robust security to the huge volume of information residing in DNA. In present scenario, security is being managed through symmetric key cryptography only. A new initiative has been taken to increase the robustness of DNA security. In this paper we are integrating public key cryptography inside traditional DNA security algorithm. The additional security is provided through a new algorithm as proposed, which takes advantage of residue theorem and traditional RSA algorithm. The main security concept is based on complexity in factorization and high versatility of choosing parameters/ variables. Basically, DNA is encrypted through symmetric key cryptography and the key used to encrypt the data symmetrically is itself encrypted asymmetrically through proposed modified RSA algorithm. Through example, it is further illustrated in this paper that this is not only one of the optimized algorithms to provide a tradeoff between security and computational speed but also adds some sort of defense strategy against various attacks in a layered approach.