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.

Alexei Petrenko is Associate Professor at the Innopolis University, PhD, and Postdoctoral researcher at the Saint Petersburg Electrotechnical University ""LETI"", Russia. Previously, Alexei Petrenko was a postdoc and a PhD student at the Innopolis University in the group of Professor Sergei Petrenko. His PhD thesis was "Quantum-Resistance in Blockchain Networks" (2020). Alexei Petrenko has closely followed the blockchain space since late 2014. His main research interests are quantum cryptanalysis in Bitcoin and off-chain protocols. Earlier, he researched secure development practices on the Ethereum platform and domain-specific languages for smart contracts. In 2016-2020, Alexei Petrenko was a researcher on code vulnerabilities of Blockchain networks. He is author and co-author of 3 monographs and more than 145 articles on information security issues, including, monographs and practical manuals for Springer Nature Switzerland AG, Athena and DMK-Press (Russia).

1. The Relevance of Practical Issues of Quantum Cryptanalysis Aimed at Improving Cyber Security and Resilience of the Digital Economy 2. Possible Implementations of the Shor Factorization Algorithm on a Quantum Circuit to Develop Requirements for Quantum Cryptanalysis Algorithms 3. Quantum Cryptanalysis Algorithms Based on Factorization and Discrete Logarithm Problems in Various Algebraic Structures 4. Examples of the Developed Promising Software Package for Quantum Cryptanalysis of Asymmetric Encryption and Digital Signature Schemes