The lesson here is that it is insufficient to
protect ourselves with laws; we need to
protect ourselves with mathematics.

Bruce Schneier (1963)

Stochastic Cryptography.
An Innovative Breakthrough in Security Provisioning

If we look at the history of development of cryptography, we are dealing today with a third wave, which provides the transition from the cryptographic primitives associated with information security of automated information systems, or, in other words, with the logic level of processing (Security Systems), to cryptographic security tools at the physical layer processing (Physical Security, Safety Systems), associated with the Protection of system elements from cloning, counterfeiting and unauthorized operations.
Unlike software solutions (used at the logical level of processing), which are not critical to the number of executable commands and the memory used, the physical layer of processing is a medium with an extreme scarcity of resources, dictated by the cost, profitability and power consumption of hardware solutions. The contradictions of this development manifest themselves in an especially acute manner as RFID technologies and microsensor technologies are being developed (Microsensor Technology, Micro-Sensor Technology).
Despite the efforts undertaken around the world (RFIDSec, ECRYPT, BRIDGE), to solve the problems dictated by an extreme scarcity of resources seems impossible today and in the near future, despite the emergence of new areas of research, i.e., Stochastic Cryptography, Minimalistic Cryptography and Light-Weight Cryptography. Apparently, in order to overcome such a nontrivial problem, innovative solutions and approaches are needed. In contrast to the well-known analogues built, first of all, on Recurrence Methods and Galois Fields, only Pre-Arithmetic based Discrete-time Stochastic Systems and Stochastic Technologies (Random Method, Stochastic Method) and Random Method (Randomization Method, Stochastic Method) as well as Stochastic Cryptography represented by these technologies have today exceptional possibilities when it comes to them.

Stochastic Technologies are based on Dichotomic Properties inherent in natural phenomena and processes cover all sections of symmetric cryptography. These technologies do not affect the cryptographic strength when they are open for review if, of course, it does not contradict commercial interests, are transparent to examination (see paper – Conference RusCrypto 2006), have an overwhelming advantage in all respects over the known analogues (see results of the analysis), yield new results and create real conditions for an innovative breakthrough in security provisioning.
The cryptographic primitives represented by the technologiesin, in particular, primitives of Generation of random numbers (Random Number Generation, RNG, PRNG, TRNG), Authentications and Ciphering (Encryption), are brought to a level of fabrication of industrial samples. Do not judge us strictly, but open publication of cryptographic primitives, intended for industrial development, until a certain time, was constrained only by danger of infringement of copyright and commercial interests.


However, the materials and developments do not limit the creativity of scientists and are capable, as shown by more than 8 years of experience of debates with engineers and scientists – from inventors to academics, to fully withstand the sweeping criticism and hasty conclusions that differ from reality.

Igor Kulakov, Игорь Кулаков