The mathematical model of signed sequences with repetitions (texts) is a multiset. The multiset was defined by D. Knuth in 1969 and later studied in detail by A. B. Petrovsky [1]. The universal property of a multiset is the existence of identical elements. The limiting case of a multiset with unit multiplicities of elements is a set. A set with unit multiplicities corresponding to a multiset is called its generating set or domain. A set with zero multiplicity is an empty set.
The previous work from ref [1] describes the method of transforming a sign sequence into algebra through an example of a linguistic text. Two other examples of algebraic structuring of texts of a different nature are given to illustrate the method.
Algebra and language (writing) are two different learning tools. When they are combined, we can expect new methods of machine understanding to emerge. To determine the meaning (to understand) is to calculate how the part relates to the whole. Modern search algorithms already perform the task of meaning recognition, and Google’s tensor processors perform matrix multiplications (convolutions) necessary in an algebraic approach. At the same time, semantic analysis mainly uses statistical methods. Using statistics in algebra, for instance, when looking for signs of numbers divisibility, would simply be strange. Algebraic apparatus is also useful for interpreting the calculations results when recognizing the meaning of a text.
Some time ago among security researchers, it was very “fashionable” to find improperly configured AWS cloud storages with various kinds of confidential information. At that time, I even published a small note about how Amazon S3 open cloud storage is discovered.
However, time passes and the focus in research has shifted to the search for unsecured and exposed public domain databases. More than half of the known cases of large data leaks over the past year are leaks from open databases.
Today we will try to figure out how such databases are discovered by security researchers...
