Quantum Safe Cryptographic Primitives Using Lattice Based Algorithms

Quantum computers will break today's most popular public-key cryptographic systems, including RSA, DSA, and ECDSA. This book introduces the reader to the next generation of cryptographic algorithms, the systems that resist quantum-computer attacks: in particular, post-quantum public-key encryption systems and post-quantum public-key signature systems. Leading experts have joined forces for the first time to explain the state of the art in quantum computing, hash-based cryptography, code-based cryptography, lattice-based cryptography, and multivariate cryptography. Mathematical foundations and implementation issues are included. This book is an essential resource for students and researchers who want to contribute to the field of post-quantum cryptography.

Quantum mechanics, the subfield of physics that describes the behavior of very small (quantum) particles, provides the basis for a new paradigm of computing. First proposed in the 1980s as a way to improve computational modeling of quantum systems, the field of quantum computing has recently garnered significant attention due to progress in building small-scale devices. However, significant technical advances will be required before a large-scale, practical quantum computer can be achieved. Quantum Computing: Progress and Prospects provides an introduction to the field, including the unique characteristics and constraints of the technology, and assesses the feasibility and implications of creating a functional quantum computer capable of addressing real-world problems. This report considers hardware and software requirements, quantum algorithms, drivers of advances in quantum computing and quantum devices, benchmarks associated with relevant use cases, the time and resources required, and how to assess the probability of success.

The accelerating pace at which quantum computing is developing makes it almost inevitable that some of the major cryptographic algorithms and protocols we rely on daily, for everything from internet shopping to running our critical infrastructure, may be compromised in the coming years. This book presents 11 papers from the NATO Advanced Research Workshop (ARW) on Quantum and Post-Quantum Cryptography, hosted in Malta in November 2021. The workshop set out to understand and reconcile two seemingly divergent points of view on post-quantum cryptography and secure communication: would it be better to deploy post-quantum cryptographic (PQC) algorithms or quantum key distribution (QKD)? The workshop brought these two communities together to work towards a future in which the two technologies are seen as complementary solutions to secure communication systems at both a hardware (QKD) and software (PQC) level, rather than being in competition with each other. Subjects include the education of an adequate workforce and the challenges of adjusting university curricula for the quantum age; whether PQC and QKD are both required to enable a quantum-safe future and the case for hybrid approaches; and technical aspects of implementing quantum-secure communication systems. The efforts of two NATO nations to address the possible emergence of cryptanalytically-relevant quantum computers are explored, as are two cryptographic applications which go beyond the basic goal of securing two-party communication in a post-quantum world. The book includes economic and broader societal perspectives as well as the strictly technical, and adds a helpful, new contribution to this conversation.

Lattice-based cryptography is a promising post-quantum cryptographic approach that can withstand potential attacks from future quantum computers. This book will introduce the theoretical mathematics that underpins lattice-based cryptography, such as the hard problems based on lattices upon which the security of lattice-based cryptosystems rely. It will provide examples of how these hard problems can be used to build basic lattice-based cryptographic primitives, namely encryption, digital signatures and key exchange, in addition to more advanced primitives such as identity-based encryption (IBE), attribute-based encryption (ABE) and hierarchical identity-based encryption (HIBE). Subsequently, the practical aspects of designing efficient and robust lattice-based cryptosystems in both hardware and software will be detailed. The resilience of lattice-based implementations to physical attacks will be discussed in addition to appropriate countermeasures that can be integrated into implementations to defend against such attacks. Finally, three case studies will be described to illustrate how lattice-based cryptography can be successfully embedded into real-world scenarios.

This book constitutes the refereed proceedings of the 6th International Workshop on Post-Quantum Cryptography, PQCrypto 2014, held in Waterloo, ON, Canada, in October 2014. The 16 revised full papers presented were carefully reviewed and selected from 37 submissions. The papers cover all technical aspects of cryptographic research related to the future world with large quantum computers such as code-based cryptography, lattice-based cryptography, multivariate cryptography, isogeny-based cryptography, security proof frameworks, cryptanalysis and implementations.

This book focuses on lattice-based cryptosystems, widely considered to be one of the most promising post-quantum cryptosystems and provides fundamental insights into how to construct provably secure cryptosystems from hard lattice problems. The concept of provable security is used to inform the choice of lattice tool for designing cryptosystems, including public-key encryption, identity-based encryption, attribute-based encryption, key change and digital signatures. Given its depth of coverage, the book especially appeals to graduate students and young researchers who plan to enter this research area.

In a world driven by technology and data, classical computing faces limitations in tackling complex challenges like climate modeling and financial risk assessment. These barriers impede our aspirations to revolutionize industries and solve intricate real-world problems. To bridge this gap, we must embrace quantum computing. Edited by Alex Khang PH, Principles and Applications of Quantum Computing is a transformative solution to this challenge. It delves into the interdisciplinary realms of computer science, physics, and mathematics, unveiling the incredible potential of quantum computing, which outperforms supercomputers by 158 million times. This technology, rooted in quantum mechanics, offers solutions to global problems and opens new frontiers in AI, cybersecurity, finance, drug development, and more. By engaging with this book, you become a pioneer in the quantum revolution, contributing to reshaping the limits of what's achievable in our digital age.