Two books by Alexey Petrenko, an associate professor at MEPhI, have been published in Russia and abroad on the current topic of post-quantum information security. Today, quantum technologies are in the spotlight of the scientific and business community. At the same time, ensuring the quantum Resilience of key digital ecosystems and platforms of the digital economy is one of the most pressing scientific and technical problems of our time. Here, quantum resilience refers to the ability of the aforementioned systems to achieve their operational goals under attacks by malicious actors using a quantum computer. The relevance of this issue is explained by the emergence of a new quantum threat to information security, the growing security requirements for critical information infrastructure, the evolving structure and behavior of the aforementioned systems, and the current inadequacy of known technologies (models, methods, and tools) for ensuring information security and cyber resilience to address the tasks of detecting, neutralizing, and preventing malicious actors’ quantum attacks. It is precisely this problem area that the books by Alexey Petrenko, associate professor at MEPhI, are devoted to.
In the monograph "Building post-quantum algebraic algorithms for EDS with two hidden groups," Alexey Petrenko spoke about breakthrough research and development in post-quantum cryptography. The solutions described in the book will help protect information and ensure the confidentiality of digital platforms of the Russian data economy in the event of cyber attacks by intruders using quantum computers.
According to the author, quantum computers will be able to crack most modern electronic digital signature schemes in the coming years. Therefore, researchers around the world are developing post‑quantum cryptographic algorithms based on various mathematical foundations — from lattices and codes to noncommutative algebras.
The existing standardized and research families of post‑quantum electronic digital signatures — lattice-based, hash-oriented, and MQ schemes — demonstrate a trade‑off between the level of security and the overhead costs of transmitting, storing, and verifying signatures, which limits their application in high‑load distributed systems. Signature schemes with a single hidden group have proven to be vulnerable. The same applies to certain schemes based on a single noncommutative structure and some semigroup schemes. Therefore, it is not enough to use one hidden group structure, and algorithms in which the cryptographic structure is complicated by two independent hidden groups are becoming a promising direction," the author notes.
In his book, Alexey Petrenko proposed and substantiated a new method for constructing post-quantum electronic digital signature algorithms based on finite noncommutative associative algebras. This scheme uses two hidden commutative groups to generate one-time exponentials, which significantly increases its cryptographic strength. For the first time, the researcher proposed an algorithmic implementation of a signature randomization method and a mechanism to protect against digital signature forgery using a single verification equation.
The monograph contains five chapters that cover the rationale and mathematical formulation of the problem, the author’s method with an assessment of its complexity and effectiveness, the development and mathematical justification of the proposed approach, recommendations for its application and practical testing, as well as the implementation of the method for ensuring the quantum resilience of digital platforms, using blockchain systems as an example.
“The book will be useful for leaders of state and commercial organizations, directors responsible for cybersecurity and cyber resilience of information infrastructure facilities and critically important applications of Russia’s digital economy, designers and planners of integrated information protection systems, as well as for postgraduate students and students at the National Quantum University,” notes Alexey Petrenko. Furthermore, in September 2026, the renowned international scientific publisher River Publishers will release Alexey Petrenko’s scientific monograph “Quantum Security: Building Quantum‑Resilient Digital Platforms for the Future,” which examines the problem statements and possible solutions for creating quantum‑resilient information systems and applications for the digital economy of the future.
First, the creation and transition to post‑quantum cryptographic primitives (Public‑Key Encryption) and Digital Signatures based on areas of mathematics that potentially contain complex computational problems for which no efficient algorithms are currently known to solve them using classical or quantum computers. This includes, among other things, approaches based on lattices, multivariate polynomials, isogenies on elliptic curves, octonions, Chebyshev polynomials, finite noncommutative associative algebras (FNCA), and others.
It should be noted that in technologically advanced countries around the world (the USA, China, Russia, the European Union, etc.), the global transition to post‑quantum cryptography has ceased to be merely a research prospect and has transformed into a scientific and engineering migration task, the timing and resources for which are directly determined by the parameters of the underlying cryptographic primitives. The existing standardized families (lattice-based, hash-oriented, and MQ schemes) demonstrate a trade-off between the level of security and the overhead costs associated with transmission, storage, and verification, which makes their use in high-load digital platforms and applications of the Data Economy of the Russian Federation associated with architectural limitations. Under these conditions, the development at MEPhI of algebraic signature schemes based on the computational complexity of systems of power equations over finite non‑commutative structures represents an independent and promising scientific direction capable of ensuring a significant reduction in the size of signatures and keys without compromising cryptographic security.
Secondly, the creation and transition to single quantum‑resistant components and connections of the aforementioned systems with mathematically provable security. This includes quantum data transmission protocols that cannot be intercepted and decrypted unnoticed, quantum key distribution (QKD) systems, quantum truly random number generators (QRNG), and so on.
Thirdly (this is a less studied but quite promising area), the creation and software‑technical implementation of fundamentally new quantum‑mechanical models of key digital ecosystems and platforms of the Data Economy of the Russian Federation based on the physical principles and laws of quantum mechanics.
The aforementioned scientific monograph discusses all three listed areas in varying degrees of detail and presents possible solutions to the scientific and technical problem under consideration.
It is significant that the scientific and technical results obtained by Alexey Petrenko make it possible to ensure a smooth transition of the modern Digital Economy from its current state to a quantum‑resistant state — that is, a state that is resistant to computer attacks by malicious actors using quantum computers and high‑ and ultra‑high‑performance von Neumann supercomputers. Thus, MEPhI has already accumulated significant scientific groundwork in the field of quantum computing, quantum programming, and post‑quantum cryptography, and is capable of becoming a scientific and educational catalyst for a technological breakthrough not only in Russia but even in the BRICS countries — a leader that unites other scientific schools, manufacturers of information security tools, system integrators, and regulators to form a national quantum‑resistant PQC ecosystem and overcome the new quantum threat to information security.
