Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Voprosy kiberbezopasnosti

Quantum Resilience Estimation Method Blockchain

Alexei Petrenko, Sergei Petrenko

Published Jan 1, 2022• 3 citations
Publisher

Abstract

Abstract Purpose of work is the development of a new method for estimating the quantum resilience of modern blockchain platforms based on the effective solution of cryptanalysis problems for asymmetric encryption schemes (RSA, El-Gamal) and digital signature (DSA, ECDSA or RSA-PSS), based on computationally difficult problems of factorization and discrete logarithm. Research method is the use of quantum algorithms providing exponential gain (eg Shor’s algorithm) and quadratic gain (eg Grover’s algorithm). Due to the fact that the class of problems solved by quantum algorithms in polynomial time cannot yet be significantly expanded, more attention is paid to cryptanalysis based on the quantum Shor algorithm and other polynomial algorithms. Results of the study include a classification of well-known algorithms and software packages for cryptanalysis of asymmetric encryption schemes (RSA, El-Gamal) and digital signature (DSA, ECDSA or RSA-PSS) based on computationally difficult problems of factorization and discrete logarithm has been built. A promising method for solving problems of cryptanalysis of asymmetric encryption schemes (RSA, ElGamal) and digital signature (DSA, ECDSA or RSA-PSS) of known blockchain platforms in polynomial time in a quantum computing model is proposed. Algorithms for solving problems of quantum cryptanalysis of two-key cryptography schemes of known blockchain platforms in polynomial time are developed, taking into account the security of the discrete algorithm (DLP) and the discrete elliptic curve algorithm (ECDLP). A structural and functional diagram of the software package for quantum cryptanalysis of modern blockchain platforms “Kvant-K”, adapted to work in a hybrid computing environment of the IBM Q quantum computer (20 and 100 qubits) and the IBM BladeCenter (2022) supercomputer, has been designed. A methodology has been developed for using the “Kvant-K” software package to assess the quantum stability of blockchain platforms: InnoChain (Innopolis University), Waves Enterprise (Waves, Vostok), Hyperledger Fabric (Linux, IBM), Corda Enterprise, Bitfury Exonum, Blockchain Industrial Alliance, Exonum (Bitfury CIS), NodesPlus (b41), Masterchain (Sberbank), Microsoft Azure Blockchain, Enterprise Ethereum Alliance, etc. Practical relevance: The developed new solution for computationally difficult problems of factorization and discrete logarithm, given over finite commutative (and non-commutative) associative algebras, in a quantum model of computing in polynomial time. It is essential that the obtained scientific results formed the basis for the development of the corresponding software and hardware complex “Kvant-K”, which was tested in a hybrid computing environment (quantum computer IBM Q (20 and 100 qubits) and/or 5th generation supercomputer: IBM BladeCenter (2022), RCS based on FPGA Virtex UltraScale (2020), RFNC-VNIIEF (2022) and SKIF P-0.5 (2021). An appropriate method for estimating the quantum stability of these blockchain platforms based on the author’s models, methods and algorithms of quantum cryptanalysis has been developed and tested. Keywords: blockchain and distributed ledger technologies (DLT), SMART contracts, blockchain security threat model, quantum security threat, cryptographic attacks, quantum cryptanalysis, quantum and post-quantum cryptography, quantum algorithms Shor, Grover and Simon algorithms, quantum Fourier transform, factorization and discrete logarithm problem, post-quantum cryptography, quantum resilience of blockchain platforms.

DOI
10.21681/2311-3456-2022-3-2-22

Related papers

Basic Algorithms Quantum Cryptanalysis

Alexei Petrenko, Sergei Petrenko

Purpose of the article: development of quantum algorithms for efficient solution of cryptanalysis problems of asymmetric encryption schemes (RSA, ElGamal) and digital signature (DSA, ECDSA or RSA-PSS), based on computationally difficult problems of factorization and discrete logarithm.Research methods: Methods of quantum cryptanalysis based on the algorithms of Shor, Grover, Simon, etc.Results: algorithms for solving problems of quantum cryptanalysis of two-key cryptography schemes in polynomial time.Practical relevance: consists in developing a solution for computationally difficult problems of factorization and discrete logarithm in polynomial time, taking into account the security of the discrete algorithm (DLP) and the discrete elliptic curve algorithm (ECDLP). The obtained scientific results formed the basis for the development of a special Software Development Kit, SDK for cryptanalysis “Kvant-K”. The Certificate of state registration of the computer program No. 2020665981 was received.

Voprosy kiberbezopasnosti•Jan 1, 2023•7 citations

A method for analyzing the functional stability of blockchain ecosystems and platforms under quantum-computing-assisted attack

Sergei Petrenko, Alexei Petrenko, Natalie M. Grigorieva +1 more

Abstract Modern national blockchain ecosystems and platforms must account for emerging quantum threats. Currently, however, there are no formalized methods for the quantitative assessment of blockchain stability under adversarial quantum attacks. The development of such a methodology enables a quantitative evaluation of quantum impacts on various ecosystem components, the establishment of resilience metrics, and the prediction of potential compromise timelines for cryptographic primitives, given the capabilities of contemporary quantum hardware. This article proposes and substantiates an original method for analyzing the quantum resilience of national blockchain ecosystems – including those based on Enterprise Ethereum Alliance, Waves Enterprise (Waves, Vostok), Hyperledger Fabric (Linux, IBM), Corda Enterprise, Masterchain, and Microsoft Azure Blockchain. The proposed framework includes: (i) a mathematical model of blockchain stability accounting for diverse attack vectors; (ii) a resilience assessment methodology based on threat, vulnerability, and risk analysis; (iii) algorithms for evaluating cryptographic strength using modified Shor’s and Grover’s quantum algorithms; and (iv) an optimized Approximate Quantum Fourier Transform (AQFT) scheme to assess the feasibility of compromising blockchain cryptographic primitives.

•May 9, 2026•0 citations

Applied Quantum Cryptanalysis

Alexei Petrenko

Today we witness an explosive growth in attention to Q-computing. Q-computing technologies, along with artificial intelligence (AI) and machine learning (ML) technologies, cloud and foggy computing, as well as technologies for collecting and streaming processing of Big Data and ETL, are constantly leading the lists of ""end-to-end"" information technologies for the digital economy of technologically developed countries of the world. One of the main reasons for this is the potential ability of quantum computers to solve some computational problems more efficiently than any of the most modern classical computers of the von Neumann architecture (supercomputers). The most expressive and interesting, from an applied point of view, examples of such problems are integer factorization, effectively performed by Shor's quantum algorithm, as well as record search in an unordered database, effectively solved by Grover's algorithm. This monograph contains the best practice for solving problems of quantum cryptanalysis to improve cyber security and resilience of the digital economy. The book discusses well-known and author's software implementations of promising quantum Shor algorithms, Grover, Simon et al. Shor's algorithm provides exponential acceleration of solving factorization problems, discrete logarithm problems (DLPs) and elliptic curve discrete logarithm problems (ECDLPs). The mentioned tasks are widely used in TLS, SSH or IPsec cryptographic applications of Internet/Intranet and IIoT/IoT networks, communication protocols based on Diffie–Hellman key agreements (dependent on the strength of the DLP or ECDLP), digital signature algorithms (DSA, ECDSA, RSA-PSS), public key encryption algorithms (El Gamal, RSA-OAEP), etc. In other words, Shor's quantum algorithm is potentially capable of violating these algorithms, and with them all the mechanisms of public-key cryptography deployed in cyberspace.

River Publishers eBooks•Feb 7, 2023•8 citations

Development of Quantum Cryptanalysis Algorithms

Alexei Petrenko, Sergei Petrenko

This chapter evaluates the stability of the modern cryptographic algorithms to clarify the tasks of cryptanalysis of asymmetric encryption schemes and digital signature based on factorization and discrete logarithm problems in various algebraic structures in a quantum computing model. It considers the features of modeling quantum cryptanalysis algorithms on a quantum scheme, and shows the differences between these algorithms and classical algorithms. The quantum algorithm is performed by implementing a series of sequential unitary operations. Grover's algorithm provides a quadratic increase in speed, while some other quantum algorithms, for example, the Shor factorization algorithm, give an exponential gain compared to the corresponding classical algorithms. Grover's algorithm is modified into an algorithm for recovering the symmetric encryption key from the message text and ciphertext. The stability of the RSA asymmetric encryption system is based on the super-polynomial computational complexity of factorization of natural numbers. However, there is a quantum algorithm whose complexity is polynomial.

River Publishers eBooks•Feb 7, 2023•3 citations

Designing Quantum-Resilient Blockchain Frameworks: Enhancing Transactional Security with Quantum Algorithms in Decentralized Ledgers

Meenal R Kale, Yousef A. Baker El–Ebiary, L. Sathiya +4 more

Quantum computing is progressing at a fast rate and there is a real threat that classical cryptographic methods can be compromised and therefore impact the security of blockchain networks. All of the ways used to secure blockchain like Rivest–Shamir–Adleman (RSA), Elliptic Curve Cryptography (ECC) and Secure Hash Algorithm 256-bit (SHA256) are the characteristic of the traditional cryptographic techniques vulnerable to attack by quantum algorithms: Shor’s and Grover’s algorithms: can efficiently break asymmetric encryption and speed up brute force attacks. Because of this vulnerability, there exists a need to develop an advance quantum resilient blockchain framework to protect the decentralized ledgers from the future threats of the quantum. This research proposes Post-Quantum Cryptography (PQC), Quantum Key Distribution (QKD) and Quantum Random Number Generation (QRNG) as a formidable architectural integration, to fortify security of blockchain. Classical encryption is replaced with PQC, QKD with secure key exchange by detecting eavesdropping, and QRNG with improving cryptographic randomness to remove the predictable key vulnerability. Only with a small loss of transaction efficiency, we increase transaction encryption accuracy, key exchange security, and resistance to quantum attacks. In this quantum enhanced blockchain design, the idea is to preserve the decentralization, transparency and security and at the same time overcome the future quantum threat. By going through rigorous analysis and comparative evaluation, we demonstrate that the approach saves blockchain networks from the emerging quantum risks to make sure that the decentralized finance, smart contracts and cross chain transactions.

International Journal of Advanced Computer Science and Applications•Jan 1, 2025•3 citations

Problem of stability of modern cryptosystems against the background of the emergence of quantum computers

V. E. Kudryashov, Andrey N. Fionov

Every year, the production of quantum computers is becoming more productive and cheaper - for example, “The Tsuchongzi” computer uses 56 qubits and is able to solve problems that highlight the possibility of quantum acceleration within a few hours, while classical supercomputers require tens of thousands of years. Currently, IBM allows any Internet user to remotely connect and work on a real quantum computer, albeit with a power of several qubits. Modern cryptography is based on the fact that it is difficult to carry out factorization of integers or discrete logarithm by classical algorithms. But with the use of Shor's algorithm on a quantum computer, these difficulties are easily bypassed. Some of the most popular cryptographic systems - RSA (integer factorization), DH (discrete logarithm), and ECDSA (elliptic curves over finite fields) - will no longer be a reliable tool for data encryption with the advent of productive quantum computers. In this article, post-quantum cryptographic systems are studied and compared with the classical RSA system.

Interexpo GEO-Siberia•May 18, 2022•0 citations
Abstract Purpose of work is the development of a new method for estimating the quantum resilience of modern blockchain platforms based on the effective solution of cryptanalysis problems for asymmetric encryption schemes (RSA, El-Gamal) and digital signature (DSA, ECDSA or RSA-PSS), based on computationally difficult problems of factorization and discrete logarithm. Research method is the use of quantum algorithms providing exponential gain (eg Shor’s algorithm) and quadratic gain (eg Grover’s algorithm). Due to the fact that the class of problems solved by quantum algorithms in polynomial time cannot yet be significantly expanded, more attention is paid to cryptanalysis based on the quantum Shor algorithm and other polynomial algorithms. Results of the study include a classification of well-known algorithms and software packages for cryptanalysis of asymmetric encryption schemes (RSA, El-Gamal) and digital signature (DSA, ECDSA or RSA-PSS) based on computationally difficult problems of factorization and discrete logarithm has been built. A promising method for solving problems of cryptanalysis of asymmetric encryption schemes (RSA, ElGamal) and digital signature (DSA, ECDSA or RSA-PSS) of known blockchain platforms in polynomial time in a quantum computing model is proposed. Algorithms for solving problems of quantum cryptanalysis of two-key cryptography schemes of known blockchain platforms in polynomial time are developed, taking into account the security of the discrete algorithm (DLP) and the discrete elliptic curve algorithm (ECDLP). A structural and functional diagram of the software package for quantum cryptanalysis of modern blockchain platforms “Kvant-K”, adapted to work in a hybrid computing environment of the IBM Q quantum computer (20 and 100 qubits) and the IBM BladeCenter (2022) supercomputer, has been designed. A methodology has been developed for using the “Kvant-K” software package to assess the quantum stability of blockchain platforms: InnoChain (Innopolis University), Waves Enterprise (Waves, Vostok), Hyperledger Fabric (Linux, IBM), Corda Enterprise, Bitfury Exonum, Blockchain Industrial Alliance, Exonum (Bitfury CIS), NodesPlus (b41), Masterchain (Sberbank), Microsoft Azure Blockchain, Enterprise Ethereum Alliance, etc. Practical relevance: The developed new solution for computationally difficult problems of factorization and discrete logarithm, given over finite commutative (and non-commutative) associative algebras, in a quantum model of computing in polynomial time. It is essential that the obtained scientific results formed the basis for the development of the corresponding software and hardware complex “Kvant-K”, which was tested in a hybrid computing environment (quantum computer IBM Q (20 and 100 qubits) and/or 5th generation supercomputer: IBM BladeCenter (2022), RCS based on FPGA Virtex UltraScale (2020), RFNC-VNIIEF (2022) and SKIF P-0.5 (2021). An appropriate method for estimating the quantum stability of these blockchain platforms based on the author’s models, methods and algorithms of quantum cryptanalysis has been developed and tested. Keywords: blockchain and distributed ledger technologies (DLT), SMART contracts, blockchain security threat model, quantum security threat, cryptographic attacks, quantum cryptanalysis, quantum and post-quantum cryptography, quantum algorithms Shor, Grover and Simon algorithms, quantum Fourier transform, factorization and discrete logarithm problem, post-quantum cryptography, quantum resilience of blockchain platforms.
Purpose of the article: development of quantum algorithms for efficient solution of cryptanalysis problems of asymmetric encryption schemes (RSA, ElGamal) and digital signature (DSA, ECDSA or RSA-PSS), based on computationally difficult problems of factorization and discrete logarithm.Research methods: Methods of quantum cryptanalysis based on the algorithms of Shor, Grover, Simon, etc.Results: algorithms for solving problems of quantum cryptanalysis of two-key cryptography schemes in polynomial time.Practical relevance: consists in developing a solution for computationally difficult problems of factorization and discrete logarithm in polynomial time, taking into account the security of the discrete algorithm (DLP) and the discrete elliptic curve algorithm (ECDLP). The obtained scientific results formed the basis for the development of a special Software Development Kit, SDK for cryptanalysis “Kvant-K”. The Certificate of state registration of the computer program No. 2020665981 was received.
Abstract Modern national blockchain ecosystems and platforms must account for emerging quantum threats. Currently, however, there are no formalized methods for the quantitative assessment of blockchain stability under adversarial quantum attacks. The development of such a methodology enables a quantitative evaluation of quantum impacts on various ecosystem components, the establishment of resilience metrics, and the prediction of potential compromise timelines for cryptographic primitives, given the capabilities of contemporary quantum hardware. This article proposes and substantiates an original method for analyzing the quantum resilience of national blockchain ecosystems – including those based on Enterprise Ethereum Alliance, Waves Enterprise (Waves, Vostok), Hyperledger Fabric (Linux, IBM), Corda Enterprise, Masterchain, and Microsoft Azure Blockchain. The proposed framework includes: (i) a mathematical model of blockchain stability accounting for diverse attack vectors; (ii) a resilience assessment methodology based on threat, vulnerability, and risk analysis; (iii) algorithms for evaluating cryptographic strength using modified Shor’s and Grover’s quantum algorithms; and (iv) an optimized Approximate Quantum Fourier Transform (AQFT) scheme to assess the feasibility of compromising blockchain cryptographic primitives.
Today we witness an explosive growth in attention to Q-computing. Q-computing technologies, along with artificial intelligence (AI) and machine learning (ML) technologies, cloud and foggy computing, as well as technologies for collecting and streaming processing of Big Data and ETL, are constantly leading the lists of ""end-to-end"" information technologies for the digital economy of technologically developed countries of the world. One of the main reasons for this is the potential ability of quantum computers to solve some computational problems more efficiently than any of the most modern classical computers of the von Neumann architecture (supercomputers). The most expressive and interesting, from an applied point of view, examples of such problems are integer factorization, effectively performed by Shor's quantum algorithm, as well as record search in an unordered database, effectively solved by Grover's algorithm. This monograph contains the best practice for solving problems of quantum cryptanalysis to improve cyber security and resilience of the digital economy. The book discusses well-known and author's software implementations of promising quantum Shor algorithms, Grover, Simon et al. Shor's algorithm provides exponential acceleration of solving factorization problems, discrete logarithm problems (DLPs) and elliptic curve discrete logarithm problems (ECDLPs). The mentioned tasks are widely used in TLS, SSH or IPsec cryptographic applications of Internet/Intranet and IIoT/IoT networks, communication protocols based on Diffie–Hellman key agreements (dependent on the strength of the DLP or ECDLP), digital signature algorithms (DSA, ECDSA, RSA-PSS), public key encryption algorithms (El Gamal, RSA-OAEP), etc. In other words, Shor's quantum algorithm is potentially capable of violating these algorithms, and with them all the mechanisms of public-key cryptography deployed in cyberspace.
This chapter evaluates the stability of the modern cryptographic algorithms to clarify the tasks of cryptanalysis of asymmetric encryption schemes and digital signature based on factorization and discrete logarithm problems in various algebraic structures in a quantum computing model. It considers the features of modeling quantum cryptanalysis algorithms on a quantum scheme, and shows the differences between these algorithms and classical algorithms. The quantum algorithm is performed by implementing a series of sequential unitary operations. Grover's algorithm provides a quadratic increase in speed, while some other quantum algorithms, for example, the Shor factorization algorithm, give an exponential gain compared to the corresponding classical algorithms. Grover's algorithm is modified into an algorithm for recovering the symmetric encryption key from the message text and ciphertext. The stability of the RSA asymmetric encryption system is based on the super-polynomial computational complexity of factorization of natural numbers. However, there is a quantum algorithm whose complexity is polynomial.
Quantum computing is progressing at a fast rate and there is a real threat that classical cryptographic methods can be compromised and therefore impact the security of blockchain networks. All of the ways used to secure blockchain like Rivest–Shamir–Adleman (RSA), Elliptic Curve Cryptography (ECC) and Secure Hash Algorithm 256-bit (SHA256) are the characteristic of the traditional cryptographic techniques vulnerable to attack by quantum algorithms: Shor’s and Grover’s algorithms: can efficiently break asymmetric encryption and speed up brute force attacks. Because of this vulnerability, there exists a need to develop an advance quantum resilient blockchain framework to protect the decentralized ledgers from the future threats of the quantum. This research proposes Post-Quantum Cryptography (PQC), Quantum Key Distribution (QKD) and Quantum Random Number Generation (QRNG) as a formidable architectural integration, to fortify security of blockchain. Classical encryption is replaced with PQC, QKD with secure key exchange by detecting eavesdropping, and QRNG with improving cryptographic randomness to remove the predictable key vulnerability. Only with a small loss of transaction efficiency, we increase transaction encryption accuracy, key exchange security, and resistance to quantum attacks. In this quantum enhanced blockchain design, the idea is to preserve the decentralization, transparency and security and at the same time overcome the future quantum threat. By going through rigorous analysis and comparative evaluation, we demonstrate that the approach saves blockchain networks from the emerging quantum risks to make sure that the decentralized finance, smart contracts and cross chain transactions.
Every year, the production of quantum computers is becoming more productive and cheaper - for example, “The Tsuchongzi” computer uses 56 qubits and is able to solve problems that highlight the possibility of quantum acceleration within a few hours, while classical supercomputers require tens of thousands of years. Currently, IBM allows any Internet user to remotely connect and work on a real quantum computer, albeit with a power of several qubits. Modern cryptography is based on the fact that it is difficult to carry out factorization of integers or discrete logarithm by classical algorithms. But with the use of Shor's algorithm on a quantum computer, these difficulties are easily bypassed. Some of the most popular cryptographic systems - RSA (integer factorization), DH (discrete logarithm), and ECDSA (elliptic curves over finite fields) - will no longer be a reliable tool for data encryption with the advent of productive quantum computers. In this article, post-quantum cryptographic systems are studied and compared with the classical RSA system.