It seems that the Chaos, in the true sense,
is not something transcendental, but obeys
strict laws, consistent with the algebraic
structures and mathematics in general.

Non-Regular Random Method, Stochastic Method and Cryptography

The Non-Regular Random Method (Stochastic Method, Randomization Method), as a component of a breakthrough innovation in the field of algebra (Pre-Arithmetic) and Stochastic Technologies (Stochastic System) – Random Method (Stochastic Method, Randomization Method), involves spreading the influence of low-order bits of the digital blocks on the high-order bits, and at the same time, bits of digital blocks include feedback. In terms of technical implementation the method is represented by non-linear shift registers (NLSR).
For improving the quality of statistical and technical specifications, these registers allow effective, multiplicative linear feedback shift register (LFSR) complexation (see Evaluation of Implementation Variants).

The Random Method (Stochastic Method) opens up new directions for the innovation development of Dynamic Systems of discrete-time and Stochastic Systems, which give birth to the Stochastic Cryptography (Minimalistic Cryptography, Light-Weight Cryptography), Binary Nonlinear Functions, One-sided Functions, One-way Functions, Hash Functions, Random Number Generators (RNG, PRNG, TRNG), Block Ciphers and Nonlinear Dynamics (Non-Linear Dynamics).



We present a method for forming non-regular binary sequences, called the Non-Regular Random Method (Stochastic Method, Randomization Method). The sequences are initial for changing and obtaining sequences with a predetermined period and properties, characteristic of stochastic (random) processes. Multi-digit devices based on this method are characterized by stable and, if necessary, one-way and functionally unpredictable behaviour, exhaustively complete parallelism and simple implementation, at the same time by very small hardware and energy costs, as well as by the extreme attainable level of performance comparable, regardless of the digits, with the speed of one or two elementary logical operations.

Scope of application: dynamic systems, digital techniques and processing; stochastic systems and devices; generation of random numbers (Random Number Generation) and data conversion (Encryption); Identification, Authentication and Authorization; processing of noise-like signals (UWB); information and communication and sensor (RFID) devices and systems (Sensor System, Sensor Technology); systems of representation and imaging of information.

Patents, Analytics and Analysis

International Patent Application «A Method for Forming Non-Regular Binary Sequences» № PCT/RU2011/000647 dated 26 August 2011. Publication No. WO 2013/028094 dated 28 February 2013.
Russion Patent № 2467378, Title Page, Bulletin № 32 dated 20 November 2012.
Specification of Patent – number search (значение): 2467378, section «Реестр Изобретений».
Description of Application. Analytics and Analysis. Kulakov I.A., Moscow, 10.12.2012.


Igor Kulakov, Игорь Кулаков