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Lattice Theory for Machine Learning
AbstractThis article presents a theoretical foundation for constructing a machine learning system based on the binary similarity operation. The key...
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Lattice codes for lattice-based PKE
Existing error correction mechanisms in lattice-based public key encryption (PKE) rely on either trivial modulation or its concatenation with error...
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Lattice basis reduction techniques
In recent years, there has been a significant amount of work conducted in the field of Lattice Basis Reduction Techniques, which is one of the...
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Security Evaluation on KpqC Round 1 Lattice-Based Algorithms Using Lattice Estimator
Post-quantum cryptography is expected to become one of the fundamental technologies in the field of security that requires public-key cryptosystems,...
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Lattice-Based Secret Sharing Scheme (Chinese Remainder Theorem)
Secret sharing schemes are used as a tool in many cryptographic protocols including revocable electronic cash, electronic voting, cloud computing and...
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Correspondence Theory on Vector Spaces
This paper extends correspondence theory to the framework of \(\mathbb {K}\)...
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A survey on lattice-based digital signature
Lattice-based digital signature has become one of the widely recognized post-quantum algorithms because of its simple algebraic operation, rich...
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Quantum Augmented Lattice Attack on NTRU with Side Information
NTRU is one of the most important lattice-based public key cryptosystems, and a potential candidate for post-quantum cryptography. This paper derives...
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A New Self-dual BKZ Algorithm Based on Lattice Sieving
Lattice reduction algorithm is an important algorithm for solving lattice Shortest Vector Problem (SVP), which makes it the primary tool for...
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Lattice Linearity of Multiplication and Modulo
In this paper, we study the lattice linearity of multiplication and modulo operations. We demonstrate that these operations are lattice linear and...
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Concrete Analysis of Quantum Lattice Enumeration
Lattice reduction algorithms such as BKZ (Block-Korkine-Zolotarev) play a central role in estimating the security of lattice-based cryptography. The...
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Approximation Fixpoint Theory in Coq
Approximation Fixpoint Theory (AFT) is an abstract framework based on lattice theory that unifies semantics of different non-monotonic logic. AFT has...
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Error Correction and Ciphertext Quantization in Lattice Cryptography
Recent work in the design of rate \(1 - o(1)\)...
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Hesitant fuzzy three-way concept lattice and its attribute reduction
Formal concept analysis is a widely studied mathematical tool for performing data analysis and processing. Three-way decision is a model of decision...
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Certificateless network coding proxy signatures from lattice
Network coding can improve the information transmission efficiency and reduces the network resource consumption, so it is a very good platform for...
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Crisp-Fuzzy Concept Lattice Based on Interval-Valued Fuzzy Sets
Fuzzy concept lattices can be viewed as the generalizations of the classical concept lattices in fuzzy formal contexts, which is a key issue and a...
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Hull Attacks on the Lattice Isomorphism Problem
The lattice isomorphism problem (LIP) asks one to find an isometry between two lattices. It has recently been proposed as a foundation for...
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Bit Security Analysis of Lattice-Based KEMs Under Plaintext-Checking Attacks
Plaintext-checking attack (PCA) is a type of attack where an adversary recovers the secret key with the help of a plaintext-checking (PC) oracle that...
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Lattice-Free Simplices with Lattice Width \(2d - o(d)\)
The Flatness theorem states that the maximum lattice width \(\mathrm {Flt}(d)\)...
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Ideal hierarchical secret sharing and lattice path matroids
By a fundamental result by Brickell and Davenport (J Cryptol 4:123–134, 1991), the access structures of ideal secret sharing schemes are matroid...
