Secure, Green Implementation of Modular Arithmetic Operations for IoT and Cloud Applications

In this chapter, methods for securely performing the calculations required for fundamental modular arithmetic operations, namely multiplication and exponentiation using mobile, embedded, remote or distant computational resources, are proposed that offer the possibility for green information processing system development. These methods are targeted to the distributed paradigms of cloud computing resources and Internet of Things applications. They provide security by avoiding the disclosure to the cloud resource of either the data or the user secret key. Simultaneously, environmental effects of processing are minimized by the simplifications of the operations and by transferring demanding calculations to energy efficient data centers. Hence the proposed methods are also shown to serve the green IT engineering paradigm. An algorithm for the software implementation of modular multiplication is proposed, which uses pre-computations with a constant modulus to reduce the computational load imposed upon the processor. The developed modular multiplication algorithm provides faster execution on low complexity hardware in comparison with the existing algorithms and is oriented towards the variable value of the modulus, especially with the software implementation on micro controllers and smart cards whose architectures include a small number of bits. The proposed technique for modular exponentiation is based on performing simple operations on the user computational resources, shifting the remaining complex operations to high performance, energy-efficient cloud resources and operates by separating the procedure for modular exponentiation in two components. Security is maintained by maintaining the purpose-specific secret key information exclusively in user resources. The details of the pre-calculation of the secret keys are described. Hence the procedure for transferring the most demanding part of the calculation to the cloud resources is given. It is therefore shown that a potential attacker receives no information by intercepting the data existing in the cloud. The overall process is illustrated by a simple numerical example. The use of the new algorithm in Information Society applications that demand security is investigated. Such applications include e-Government, e-Banking, e-Commerce etc. The algorithm is shown to be adequate both for the applications for which it was originally intended, as well as for applications that are much more demanding in the level of security they require, such as military applications.