Information Society aims to promote innovation in the context of governmental and enterprise information systems and participation of the majority of the general population. An important prerequisite for the penetration and widespread use of Information Society technologies is to enhance the perception of security that these technologies offer without making them inaccessible to users with limited computational resources. In this paper a new 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 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.