A survey that frames the security of lattice-based post-quantum cryptography as classical geometry-of-numbers problems: SVP/CVP, ball packing and covering, and quadratic forms.
A Survey on Post-Quantum Cryptography: State-of-the-Art and Challenges
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abstract
The paper explains that post-quantum cryptography is necessary due to the introduction of quantum computing causing certain algorithms to be broken. We analyze the different types of post-quantum cryptography, quantum cryptography and quantum-resistant cryptography, to provide a thorough understanding of the current solutions to the problems and their limitations. We explain the current state of quantum computing and how it has changed over time while discussing possible attacks on both types of post-quantum cryptography. Next, current post-quantum algorithms are discussed, and implementations are demonstrated. Lastly, we conclude that due to quantum cryptography's present limitations it is not a viable solution like it is often presented to be and that it is currently better to use quantum-resistant cryptography.
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2025 1verdicts
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Some Mathematical Problems Behind Lattice-Based Cryptography
A survey that frames the security of lattice-based post-quantum cryptography as classical geometry-of-numbers problems: SVP/CVP, ball packing and covering, and quadratic forms.