Turing Machine: At the Origins of Computer Science and Cryptography

Turing's machine was a grand invention that marked the beginning of the era of information technology and anticipated the architecture of modern computer systems. In less than twenty-four years, the outstanding British mathematician and analyst Alan Turing managed to mentally construct an abstract mechanism for solving one of the fundamental problems of mathematics, which was formulated by the famous German professor David Hilbert at the International Mathematical Congress held in 1900 in Paris.

Turing Machine

The Turing machine not only became a clear answer to a specific computational problem, but also became the theoretical basis of the algorithms and the scientific base of programming. In addition, the very principle of solving complex mathematical problems by constructing various abstract mechanisms and constructing algorithms executed by electronic devices formed the basis for the emergence of a new field of intellectual activity - information technology.

The Turing machine is equipped with an endless ribbon divided into cells, each of which contains a symbol from a fixed finite set. The collection of all characters is called the alphabet of the machine. One of the characters of this peculiar alphabet stands out and is called the “space”. The Turing machine changes the contents of the cells using a special reading and writing head moving along the tape. Receiving information from the head about the contents of each cell, the device decides, depending on its internal state, which character to write in this cell and where to move the head after this operation. In this case, the internal state (memory) of the machine, characterized by a certain value from zero to a certain maximum value, also undergoes a change.

Universal Turing Machine

The Turing machine is extremely simple, but it allows you to run almost any program built on clear algorithms. To perform various computational operations, there is a special table in which certain rules are written, which are a set of universal instructions for the machine. Guided by this table, in which the order of actions for a particular combination of different states and symbols is fixed, the device determines which computational operation should be performed in each specific situation. In fact, the universal Turing machine is the first prototype of modern computers.

Nondeterministic Turing Machine

The ingenious invention of Alan Turing was successfully used by the British cryptanalytic bureau during World War II to crack German secret codes. Often, the decryption of the secret messages of the underwater vultures Doenitz lay on the Churchill table before getting into the Reich Chancellery. Unlike German cryptographers who practiced a purely intuitive approach and treated cryptography as an art, Alan Turing's methodology provided algorithmic methods for solving complex problems of decrypting secret codes, which turned out to be incomparably more effective.

The non-deterministic Turing machine made it possible to crack the adversary’s ciphers not only to ingenious cryptographers, but also to ordinary employees of the bureau, turning intuitive actions into a planned targeted movement toward the target. The data obtained using the Turing machine to a large extent influenced the outcome of the battle for England.

Source: https://habr.com/ru/post/G30713/


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