Sensitive information is transmitted across the internet every day and keeping such information as sacred is an important adventure. This is because malicious activities are on the increase as hackers are doing everything possible to steal such information. Rivest Shamir Adleman (RSA) encryption is the most widely used for securing sensitive information sent over an insecure channel like the internet. However RSA has a difficult problem of encrypting smaller messages, m for which me < n, where e is the public component and n, the modulus.

This work presents several schemes for enhancing RSA encryption algorithms. First, an improved RSA cryptosystem based on Mixed Radix Conversion (MRC) was designed and implemented. This scheme utilizes two stages of encryption. The first stage is the traditional RSA and the second stage is to further encrypt the cypher text obtained from RSA using smaller moduli. The first stage of the decryption process is to obtain a partial result through MRC. The final stage of decryption is the classical RSA decryption process. This is to enable a message m, for which me < n to be encrypted. The obtained results indicated that the proposed system outperforms the existing algorithm in terms of security when the message, 2 is to be encrypted. The private key length of the proposed scheme was found to be10 -- bit longer than the classical RSA encryption scheme. This indicates that the proposed scheme has the ability to withstand brute force attack than the classical RSA encryption scheme. Secondly, a new RSA encryption scheme based on the Chinese Remainder Theorem (CRT) with a high dynamic range was implemented. This is achieved by designing and implementing a scheme with two levels of encryption and a corresponding two level of decryption. The first level of encryption is the classical RSA encryption and in the second level of encryption, forward conversion technique is utilize first level of decryption, the CRT is employed and the classical RSA decryption process was utilized for the second level of decryption. Encrypting messages m ≤ 20 were found not to be secured using RSA scheme. However, encrypting same messages using the proposed scheme was found to be secured. The proposed scheme performs better than the state of the art in terms of propagation delay and cost. The propagation delay and cost of the state of the art are (12n + 10)FA and (15n + 5)DFA respectively, whiles the delay and cost of the proposed system are (12n +3)DFA and (16n -- 2)DFA respectively.Next, a new MRC based RSA with error detection and correction scheme is presented. Length-five moduli set is used where the first three are the information moduli and the last two are the redundant moduli. A forward converter is built using the information moduli set for purposes of data encryption in the second stage of encryption. MRC is employed to build a reverse converter using the information moduli set that will be used for the decryption process. How the scheme detects and corrects an error is demonstrated. This scheme is found to detect and correct a maximum of (2n+1) --- bits errors occurring in the first modulus or the second modulus. This ensures a more reliable data communication using the proposed system than the RSA scheme. Finally, a RNS decoder pair is designed using a length-two moduli set for purposes of data compression and secured communication. This scheme was found to reduce the number of bits in a message to 40?46.15% of its original size for larger messages and 14.29% for relatively smaller messages. This greatly decreases the traffic of the channel and hence increases the speed of transmission. This also reduces the transmission power needed to send data packets across the transmission c.