SoK: Systematizing Hybrid Strategies for the Transition to Post-Quantum Cryptography

James Howe, Thomas Prest, Daniel Apon

R. D. N. Shakya, Chaman Wijesiriwardana, Sugandima Vidanagamachchi +1 more

Biming Zhou, Yiting Liu, Haodong Jiang +1 more

Sunday Oladele, Lamide Kumibe

Andrea Basso, Joppe W. Bos, Jan-Pieter D’Anvers +9 more

The Learning with Rounding (LWR) problem, introduced as a deterministic variant of Learning with Errors (LWE), has become a promising foundation for post-quantum cryptography. This Systematization of Knowledge (SoK) article presents a comprehensive survey of the theoretical foundations, algorithmic developments, and practical implementations of LWR-based cryptographic schemes. We introduce LWR within the broader landscape of lattice-based cryptography and post-quantum security, highlighting its advantages such as reduced randomness, improved efficiency, and enhanced side-channel resistance. We explore the evolution of security reductions from LWR to LWE, including recent advances that support practical parameter regimes and address challenges in both bounded and unbounded sample settings. This article systematically reviews existing LWR-based schemes — including Saber, Lizard, Florete, Espada, Sable, and SMAUG — analyzing their design choices, parameter sets, and performance tradeoffs. Furthermore, we examine the impact of LWR on side-channel resistance, failure probabilities, and masking efficiency, demonstrating its suitability for secure and efficient implementations. By consolidating the research spanning theory and practice, this SoK aims at guiding future cryptographic design and standardization efforts leveraging LWR.

Preetham Konda Nagaraja

The rapid advancement of quantum computing presents both unprecedented opportunities and significant threats to modern cybersecurity. As quantum processors progress toward practical large-scale deployment, widely used cryptographic systems, particularly RSA, ECC, and other public-key mechanisms, face the risk of becoming obsolete. This review examines how quantum technologies can be strategically leveraged to enhance cybersecurity while simultaneously addressing the vulnerabilities introduced by quantum-enabled attacks. A systematic analysis of 35-40 peer-reviewed studies was conducted to evaluate developments in post-quantum cryptography, quantum-resistant security protocols, Quantum Key Distribution (QKD), and hybrid classical–quantum defense architectures. The findings reveal a rapidly evolving research landscape focused on resilient lattice-based cryptography, scalable quantum-safe communication frameworks, and early-stage quantum machine learning applications for intrusion detection. The review highlights both the promise and current limitations of quantum-driven security solutions, including hardware constraints, integration challenges, and the need for global standardization. The study underscores the urgency for governments, industries, and researchers to adopt quantum-ready cybersecurity strategies and accelerate the transition to quantum-resilient infrastructures.