Applied Quantum Cryptanalysis

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. Cover Half Title Series Title Copyright Contents Foreword Preface Acknowledgments List of Figures List of Tables List of Abbreviations Glossary Introduction 1 The Relevance of Quantum Cryptanalysis 1.1 National Quantum Programs 1.2 The Available Scientific Groundwork 1.3 Limiting Possibilities of Cryptanalysis Methods 1.4 The Quantum Threat of Blockchain 1.5 Requirements for Quantum Cryptanalysis 1.6 Verbal Statement of the Research Problem Conclusions on Chapter 1 2 Implementation of the Shor Algorithm on a Quantum Circuit 2.1 Applicability of Fourier transforms 2.2 Reformulation of the Factorization Problem 2.3 Shor Algorithm Modification 2.4 Estimating the Quantum Resources Needed 2.5 Example Implementation of Shor’s Algorithm 2.6 Features of the Implementation of the Shor Algorithm 2.7 The Mathematical Task Definition Conclusions on Chapter 2 3 Development of Quantum Cryptanalvsis Algorithms 3.1 Assessment of the Durability of Modern Cryptographic Algorithms to Clarify the Cryptanalysis Tasks of Asymmetric Encryption Schemes (RSA or El Gamal) and Digital Signature (DSA, ECDSA, or RSA-PSS) in a Quantum Computing Model 3.2 Implementation of Cryptanalysis Algorithms 3.3 Implementation of the Shor Factorization Algorithm 3.4 Implementation of the Grover’s Search Algorithm 3.5 Development of an Algorithm for Recovering a Symmetric Encryption Key 3.6 Development of an Algorithm for Cryptanalysis of the RSA Asymmetric Encryption System 3.7 Development of an Algorithm for Cryptanalysis of the El Gamal System Conclusions on Chapter 3 4 Development of the "Q-Cryptanalysis” Platform 4.1 Features of the Implementation of the “Q-Cryptanalysis” platform 4.1.1 Q-cryptanalysis platform development tools 4.1.2 Q-cryptanalysis platform architecture 4.1.3 Example of “Q-cryptanalysis” platform operation 4.2 Features of the used Quantum Computing Model. 4.3 Testing of the “Q-Cryptanalysis” Platform 4.4 The Evaluation of the Effectiveness of the “Q-Cryptanalysis” Platform 4.5 Possible Development Directions of the “Q-Cryptanalysis” Platform 4.6 A Feasibility Study for the Development of the “Q-Cryptanalysis” Platform Conclusions on Chapter 4 Conclusion References List of Open Training Courses in WWW Websites of Manufacturers Of Quantum Computers And Simulators Archives of Quantum Algorithms and Simulators List of Well-known National Quantum Programs Index About the Author Publications Projects