Then of The thee in me who works behind
The Veil, I lifted up my hands to find
A lamp amid the Darkness; and I heard,
As from Without – «The me within thee blind!».

Omar Khayyan (1048-1181), RUBAIYAT

Random Method, Stochastic Method


The Random Method (Stochastic Method, Randomization Method) is based on a fundamental basis, provided by Pre-Arithmetic (Prearithmetic) and by innovative Stochastic Technologies.
The Random Method (Stochastic Method) offers new directions of innovative development of Dynamic discrete-time systems, Stochastic Systems and Stochastic Cryptography (Minimalistic Cryptography, Light-Weight Cryptography), Binary Nonlinear Functions, One-Sided Functions, One-Way Functions, Hash Functions, Nonlinear Dynamics (Non-Linear Dynamics) as well as of digital technologies following from them that cover, to the highest or difference degree, ordered and harmonious, chaotic and random, stationary and nonstationary processes inherent in nature. This is directly confirmed by the Polynomial Congruential Method and Its Nonlinear Extensions which are related to arithmetic in the most direct way (Linear, Quadratic, Cubic, Polynomial, Congruential, Method) and Congruential and Random Generators represented by them.

The Random Method (Stochastic Method) can be used to endow real objects with dual, stochastic, less or more strongly pronounced functional and statistic, linear and nonlinear, regular and non-regular, deterministic and non-deterministic, transcendent and immanent properties inherent in harmonic and chaotic random phenomena and processes.

The Random Method (Stochastic Method) is divided into regular and non-regular. In the regular method, the influence of low-order bits of the digital blocks on high-order bits of strictly unidirectional, laminar character. In the non-regular method, the digits of digital blocks possess, all in all, feedbacks.
The Regular Random Method (Stochastic Method) is used to construct Dichotomic Generators and to form n-bit binary sequences, endowed with a special structure, similar to that of a binary tree, called Dichotomic Sequence, with a repetition period of формула. In turn, Dichotomic Generators can be linked and form networks and compositions of any structural and functional complexity, as well as provide the basis for constructing high-quality Random Number Generators (RNG, PRNG, TRNG), Stream Ciphers and Stochastic discrete-time systems for various applications.

The Non-Regular Random Method (Stochastic Method) is wider, inherits structural and functional properties of the regular method, lays the ground for constructing Block Ciphers and, in its characteristics and statistical parameters, is directly associated with the ideal Chaos and truly random processes.

Non-linear shift registers (NLSR) form the kernel of the Random Method (Stochastic Method) based on the algebraic systems of Incomplete Arithmetic and Pre-Arithmetic and on the similarity to well-proven Recurrence Methods and approaches in Galois Fields.

Although this trend is still young, it is already well developed and has circuit solutions required for the manufacture of highly profitable industrial samples, which statistically, functionally and technically far ahead of all counterparts known today, i.e., including counterparts that are based on linear (LFSR) and nonlinear (NFSR) feedback shift registers and feedback with carry shift registers (FSCR), as indicated by the studies and calculations.

The Random Method (Stochastic Method) brings the solutions of traditional problems to a qualitatively new level, offers new possibilities and trends in the field of development of Dynamic Systems, Cryptography, Stochastic, Information, Communication and Sensor (RFID) Technologies, as well as of Data-Display Technologies and Systems.
Devices based on this method are designed for any platform and allow parallel processing for each of the individual binary digits of digital blocks at a rate comparable with the performance of one or two logical operations. Besides, such devices have a high tolerance for breaking their internal state and degeneracy, differ from the counterparts in the fact that they possess an overwhelming superiority in performance and a simple topology, are characterized by a very small hardware and energy costs.
The above said is particularly important under conditions of extreme scarcity of resources and ultra-fast processing, especially when the built-in protection of radio-frequency (RFID) tags, smart carts (chips) and microsensors from cloning and counterfeiting is employed.

Igor Kulakov, Игорь Кулаков