RSA Asymmetric Cryptosystem beyond Homogeneous Transformation Prince Oghenekaro Asagba, Enoch O. Nwachukwu Department of Computer Science, University of Port Harcourt, PMB 5323, Port Harcourt, Rivers State, Nigeria ([email protected]), Abstract The Internet is an insecure open network and its use and connectivity have witnessed a significant growth, and this has made it vulnerable to all forms of attacks. A threat to a network can cause harm or interrupt the network. In this paper, we looked at the security of data and message, using asymmetric cryptography, with regard to secret communication over an insecure network. Rivest, Shamir, and Adleman (RSA), is an asymmetric cryptosystem. Our work is an extension and modification of the RSA cryptosystem. What is actually being sent across the insecure network is the encrypted data. In carrying out this research, the methodology we have adopted is the Structured Systems Analysis Method (SSADM). RSA is based on homogeneous encryption, which means that the message to be encrypted does not undergo any form of transformation or encoding prior to encryption and the level of encryption is one. In our work, we extended the level of encryption to two, which makes it heterogeneous. Prior to encryption, the message is subjected to an encoding mechanism using ‘Delta Encoding Technique’. We developed a number of programs for: prime number generation, pre-computation of public and private keys, and privacy, using Turbo C++ 4.5. Our work was able to address up to 32 bits. The objective of this paper is to develop an encryption scheme which is heterogeneous compared with the current RSA system that is homogeneous, which brings us toward improved RSA cryptosystem for privacy in terms of the level of transformation. Keywords: Cryptosystem, Internet Security, Encryption, Decryption, Homogeneous, Heterogeneous ___________________________________________________________________________________ 1.0 Introduction Security is a system of safeguards designed prominent because the communications to protect a computer system and data from channels are vulnerable and subject to attack deliberate or accidental damage or access by by intruders since it involves open unauthorized persons [4]. Security of communication traffic. A network, or information is not a new phenomenon. It is as communications network, is a system of old as civilization. Security of information was interconnected computers, telephones, or other born out of the consciousness to have private commutations devices that can communicate transmission. The first communication with one another and share applications and channels were based on trustworthy data [7]. A computer network is a collection of messengers. The security of the communication communicating computers and the channels rely strictly on the messengers. With communicating media connecting them [13]. the advent of computers and computer The Internet is an insecure open network. networks, the issue of security became more West African Journal of Industrial and Academic Research Vol.Vol.9999 No.1 December 2012013333 3 Security is a broad topic that ranks almost first one key by examining the other. Usually, two in a computer networked environment [1]. The large primes are selected to compute the keys. only system that is truly secure is the one that If any of the two prime factors of a is switched off and unplugged [11]. A system participant’s public RSA-modulus can be is secure if it adequately protects information found, then the private key of that participant that it processes against unauthorized can be found, and the system is considered to disclosure, unauthorized modification, and be broken. If the primes are properly chosen unauthorized withholding (also called denial of (that is large enough), then finding them given service) [9]. In today’s heavily networked only their product (the RSA-modulus) is environment, we must guard against both believed to be a computationally infeasible obvious and subtle intrusions that can delete or task. To make the system secure, the primes corrupt vital data [8] by using appropriate chosen must be sufficiently large. On the other encryption technologies. hand, large primes imply a large RSA- Cryptography is one of the technological modulus, which leads to substantial means to provide security to data being computational overhead when using the RSA transmitted on information and system. Thus, in RSA there is a trade-off communications systems. Cryptography is between security and efficiency: on the one especially useful in the cases of financial and hand, moduli must be large for security; on the personal data. Hence, information security is a other hand, small moduli are preferred for precondition of e-application systems when efficiency. How large they have to be, depends communicating over untrusted medium like the on the speed of so-called factorization Internet [3]. algorithm [5]. In this paper, we focused on Cryptosystems is considered to be the privacy and secrecy only. In our work, we collection of encryption and decryption extended the level of encryption to two, which systems, the key generator, as well as the makes it heterogeneous. Prior to encryption, protocols for key transmission [12]. The term the message is subjected to an encoding cryptosystems is used to describe mechanism using ‘Delta Encoding Technique’. cryptographic algorithms and their The objective of this paper is to develop an characteristics. encryption scheme which is heterogeneous The introduction of public-key cryptography compared with the current RSA system that is by Diffie and Hellman in 1976 was an homogeneous. important watershed in the history of cryptography. The work sparked off interest in 2.0 Problem Statement the cryptographic research community and When a message is sent across an insecure soon several public-key schemes were network, it is most likely to pass through a proposed and implemented. The RSA, being number of machines on the way. Any of these the first realisation of this abstract model, is the machines is capable of reading and recording most widely used public-key scheme today [2]. the message for future use, and this do not The RSA cryptosystem, named after its portray privacy. In reality, people would prefer inventors R. Rivest, A. Shamir, and L to have their message(s) concealed, so that they Adleman, is the most widely used public-key should be able to send a message that can only cryptosystem. It may be used to provide both be read by the intended recipient. The quest for secrecy and digital signatures and its security is privacy has motivated researchers to adopt the based on the intractability of the integer techniques of cryptography in sending secure factorization problem [10]. RSA is an message(s), which RSA addresses. RSA tries to asymmetric cryptosystem. Asymmetric proffer solutions using cryptography based on cryptosystems involves two keys - a private the following: homogenous transformation, key and a public key that are mathematically block cipher, and deterministic encryption related. A message encrypted with one key can scheme. be decrypted only with the other. It is Many steps can be taken to prevent extremely difficult to determine the value of unauthorized access to organizational data and West African Journal of Industrial and Academic Research Vol.Vol.9999 No.1 December 2012013333 4 networks, but no network is completely safe We can describe such encryption as [6]. The issue of homogenous transformation, homogeneous since the level of encryption is block cipher, and deterministic encryption one. comes into focus. In existing open networks, such as the RSA, there are security problems Heterogeneous Encryption associated with secret communication and After the message m has been prepared to an digital signature. Threats and attacks may integer form, it undergoes a form of occur as a result of communications over an transformation or encoding before encryption open insecure network. The problem of commences. This type of encryption can be security on an open network like the Internet described as heterogeneous since the level of has been of much concern to the society. This encryption or transformation exceeds one. paper looked at RSA’s homogenous c = Fe mod n transformation. Where: c is the ciphertext based on F, F is the 3.0 Materials and Method transformed message, e is public key, n is We developed a number of programs for: modulus. prime number generation, pre-computation of public and private keys, and privacy, using 3.1 RSA Algorithms for Secret Turbo C++ 4.5. The capacity of the compiler Communication of the Existing RSA System and computer is less than 32 bits and could not RSA algorithms for privacy for the existing address or accept values above 232 for p and q system include: algorithm for key generation respectively. Our work was able to address up and algorithm for asymmetric encryption. to 32 bits. Looking from a software engineering • Algorithm for Key Generation perspective, a number of design methodologies If communication must exist between two suitable for asymmetric cryptosystems have entities, each entity must be capable of creating been put forward. They include modern an RSA public key and a related private key. structured design, Structured Entity X does the following: Systems Analysis Method (SSAM), (a) Generate any two large prime numbers, p Prototyping, Object-oriented Design, Rapid and q having approximately the same size. Application Development (RAD), Joint (b) Compute n = pq and z = (p-1) (q-1). Application Development (JAD), and (c) Compute public key, e, by choosing any Structured Systems Analysis and Design number that is relatively prime with z such that Methodology (SSADM). The methodology we e has no common factors with z. have adopted in our research is the structured (d) Compute private key, d, by solving the systems analysis method. equation: e x d = 1 (mod z). Present Procedure of RSA That is, e x d is the smallest elements in the We looked at the existing procedure of RSA series z+1, 2z+1, 3z+1, etc., that is divisible by asymmetric cryptosystems.