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The Mathematical Foundation of Post-Quantum Cryptography [PDF]

Research
In 1994, P. Shor discovered quantum algorithms that can break both the RSA cryptosystem and the ElGamal cryptosystem. In 2007, a Canadian company D-Wave demonstrated the first quantum computer.
Chuanming Zong
doaj   +2 more sources

Preface to special topic on lattice-based cryptography. [PDF]

Natl Sci Rev, 2021
Yu Y.
europepmc   +4 more sources

Some Mathematical Problems Behind Lattice-Based Cryptography

Cryptography
In 1994, P. Shor discovered quantum algorithms that can break both the RSA cryptosystem and the ElGamal cryptosystem. In 2007, D-Wave demonstrated the first quantum computer.
Chuanming Zong
doaj   +3 more sources

New bounds of the smoothing parameter for lattices. [PDF]

PLoS ONE
The smoothing parameter on lattices is crucial for lattice-based cryptographic design. In this study, we establish a new upper bound for the lattice smoothing parameter, which represents an improvement over several significant classical findings. For one-
Heng Guo, Fengxia Liu, Linlin Wang, Kun Tian   +3 more
doaj   +2 more sources

On Advances of Lattice-Based Cryptographic Schemes and Their Implementations

Cryptography, 2022
Lattice-based cryptography is centered around the hardness of problems on lattices. A lattice is a grid of points that stretches to infinity. With the development of quantum computers, existing cryptographic schemes are at risk because the underlying ...
Harshana Bandara, Yasitha Herath, Thushara Weerasundara, Janaka Alawatugoda   +3 more
doaj   +1 more source

R-LWE-Based Distributed Key Generation and Threshold Decryption

Mathematics, 2022
Ever since the appearance of quantum computers, prime factoring and discrete logarithm-based cryptography have been questioned, giving birth to the so-called post-quantum cryptography.
Ferran Alborch, Ramiro Martínez, Paz Morillo   +2 more
doaj   +1 more source

Improved Plantard Arithmetic for Lattice-based Cryptography

Transactions on Cryptographic Hardware and Embedded Systems, 2022
This paper presents an improved Plantard’s modular arithmetic (Plantard arithmetic) tailored for Lattice-Based Cryptography (LBC). Based on the improved Plantard arithmetic, we present faster implementations of two LBC schemes, Kyber and NTTRU, running ...
Junhao Huang, Jipeng Zhang, Haosong Zhao, Zhe Liu, Ray C. C. Cheung, Çetin Kaya Koç, Donglong Chen   +6 more
doaj   +3 more sources

NTT and Inverse NTT Quantum Circuits in CRYSTALS-Kyber for Post-Quantum Security Evaluation

Applied Sciences, 2023
The emergence of quantum computers threatens current cryptographic systems, and NIST is preparing for the post-quantum era through the post-quantum cryptography (PQC) contest. CRYSTALS-Kyber is a lattice-based cipher suite that is used as a PQC standard.
Gyeongju Song, Kyungbae Jang, Siwoo Eum, Minjoo Sim, Hwajeong Seo   +4 more
doaj   +1 more source

Lattice‐based cryptosystems in standardisation processes: A survey

IET Information Security, 2023
The current widely used public‐key cryptosystems are vulnerable to quantum attacks. To prepare for cybersecurity in the quantum era, some projects have been launched to call for post‐quantum alternatives.
Anyu Wang, Dianyan Xiao, Yang Yu
doaj   +1 more source

Cryptography: Advances in Secure Communication and Data Protection [PDF]

E3S Web of Conferences, 2023
In the innovative work secure communication and data protection are being main field, which are emerged by cryptography as a fundamental pillar. Strong cryptographic methods are now essential given the rising reliance on digital technologies and the ...
Victor Melvin, Praveenraj D. David Winster, R Sasirekha, Alkhayyat Ahmed, Shakhzoda Abdullayeva   +4 more
doaj   +1 more source