A Memory Optimized Public-Key Crypto Algorithm Using Modified Modular Exponentiation (MME)

Introduction With the awareness that the world is fast becoming a global village due to the increased application of the internet especially in the area of e-commerce and m-commerce, information security is an issue that cannot be overemphasized. Since the onset of e-commerce in the mid 90s, statistics have it that e-commerce is expected to generate a total sales of about $105 billion in the United States alone by 2007. Statistics further shows that as of 2001, over $700million has been lost to online sales (Holcombe, 2006). Most often times, ecommerce customers are often concerned about the authenticity of the online trader they are dealing with (data origin authenticity) and more importantly, the privacy of their information (data confidentiality); such as credit card details, which is being used for the transaction. Based on these statistics, it has become very important to improve techniques used for information security. New techniques have been developed and newer techniques are evolving. Cryptography is one of such techniques being used to ensure information security. It would be pertinent to seek ways of improving this technique as adversaries are daily developing newer techniques of breaking information security systems. Based on this, it has become pertinent to ensure security of information. Data encryption using cryptographic techniques is a means of achieving this. Furthermore, with respect to an already developed application in our laboratory- (the [M.sub.2] agent for the stock market) (Oluwatope, Aderounmu, Akande, & Adigun, 2004), an important aspect yet to be added is security of data traversing the network. The mobile agent in the stock market application traverses the Internet searching for stock deals based on certain criteria set by the stock broker. When such criteria are met, the mobile agent reports back to the static agent. Whenever a mobile agent is reporting back to the static agent, the data it is carrying along can be intercepted and altered if proper encryption scheme is not put in place. It will not be a out-of-place to mention that the proposed algorithm is applicable in digital signal processing (DSP) (Tang et al, 2003). In DSP, coding of digitised signals for optimised transmission, higher bandwidth utilisation and efficient processor-time utilisation is highly desirable. The outcome of this work will form a baseline input into algorithms used for coding and decoding in DSP. Cryptography is about communication in the presence of adversaries (Rivest, 1990). The reason for cryptography is to ensure security as information traverses an unsecured channel. Some of the objectives of information security include privacy, confidentiality, data integrity, data origin authentication, entity authentication, non-repudiation (Rivest, 1990). Basically, cryptography seeks to address these objectives in theory and in practice. Cryptography is defined as the study of mathematical techniques related to aspects of information security such as confidentiality, data integrity, entity authentication, and data origin authentication (Menezes, Van Oorschot, & Vanstone, 1997). Motivation As mentioned earlier, in the course of trying to achieve security of information, some cryptographic tools are used. These tools transform the information such that the encrypted information becomes meaningless to an adversary. The transformation process involves the execution of some computational steps. It has also been observed that the computational speed of some of these public-key cryptosystems is based on the speed of the modular exponentiation algorithm, especially when considering public-key encryption schemes such as RSA, Rabin and EIGamal. Furthermore, based on the fact that part of the security of these systems is the use of very large integers in the range of 1024bits and above, it usually requires enormous amount of processor time to complete these computational steps. …