Disposable credit card numbers are a recent approach to tackling the severe problem of credit card fraud, nowadays constantly growing, especially in the context of e-commerce payments. Whenever we cannot rely on a secure communication channel between cardholder and issuer, a possibility is to generate new numbers on the basis of some common scheme, starting from a shared secret information. However, in order to make the approach meaningful from a practical point of view, the solution should guarantee backward compatibility with the current system, absence of new investments in dedicated hardware, wide-spectrum usability, and adequate security level. In this paper, we propose a solution based on the use of standard mobile phones, fully meeting the above desiderata. Importantly, our solution does not require any cryptographic support and, as a consequence, the use of PADs or smart phones, opening then its usability to a wider potential market.

In this study, for quantifying and comparing the complexity of the digits of irrational numbers, we used the first one million digits to calculate the fractal dimensions of the digits of ten irrational numbers with long sequence of known digits via box-counting al-gorithm. The irrational numbers we studied are five algebraic numbers (