Weak Approximable Concepts and Completely Algebraic Lattices

2011 ◽  
pp. 683-689 ◽  
Author(s):  
Hongping Liu ◽  
Qingguo Li ◽  
Lankun Guo
Keyword(s):  
Algebraic Lattices

Trace form associated to cyclic number fields of ramified odd prime degree

2019 ◽  
Vol 19 (04) ◽  
pp. 2050080
Author(s):  
Robson R. Araujo ◽  
Ana C. M. M. Chagas ◽  
Antonio A. Andrade ◽  
Trajano P. Nóbrega Neto
Keyword(s):  
Number Field ◽  
Number Fields ◽  
Trace Form ◽  
Prime Degree ◽  
Ring Of Integers ◽  
Algebraic Lattices ◽  
Center Density

In this work, we computate the trace form [Formula: see text] associated to a cyclic number field [Formula: see text] of odd prime degree [Formula: see text], where [Formula: see text] ramified in [Formula: see text] and [Formula: see text] belongs to the ring of integers of [Formula: see text]. Furthermore, we use this trace form to calculate the expression of the center density of algebraic lattices constructed via the Minkowski embedding from some ideals in the ring of integers of [Formula: see text].

On the Optimality of Finite Constellations from Algebraic Lattices

2001 ◽  
Vol 6 ◽  
pp. 271-280 ◽  
Author(s):  
J.Carmelo Interlando ◽  
Michele Elia ◽  
Trajano Pires da Nóbrega Neto
Keyword(s):  
Algebraic Lattices

Well-rounded algebraic lattices in odd prime dimension

2018 ◽  
Vol 112 (2) ◽  
pp. 139-148
Author(s):  
Robson R. de Araujo ◽  
Sueli I. R. Costa
Keyword(s):  
Algebraic Lattices ◽  
Prime Dimension

scholarly journals The category of complete algebraic lattices

1972 ◽  
Vol 13 (3) ◽  
pp. 332-338 ◽  
Author(s):  
Ladnor Geissinger ◽  
William Graves
Keyword(s):  
Algebraic Lattices

scholarly journals Research of expediency of application of AVX512 for modern digital signature schemes implementations

2021 ◽  
pp. 141-145
Author(s):  
Olena Kachko ◽  
Serhiy Kandiy
Keyword(s):  
Digital Signature ◽  
Main Attention ◽  
Signature Schemes ◽  
Electronic Signature ◽  
Electronic Signatures ◽  
Algebraic Lattices ◽  
Third Stage ◽  
Numerical Transformation ◽  
Software Implementations ◽  
Lattice Based Cryptography

The third stage of the NIST PQC competition is currently underway, which aims to create new post-quantum standards in cryptography. The vast majority of finalists are representatives of lattice-based cryptography. Electronic signatures include the CRYSTALS-Dilithium schemes. This paper investigates the feasibility of using AVX512 to optimize software implementations of NIST PQC finalists among electronic signatures on algebraic lattices. Since the most expensive operation in such schemes is the multiplication of polynomials, the main attention is paid to the optimization of this operation. In particular, the method of realization of theoretical and numerical transformation using AVX512 for electronic signature schemes CRYSTALS-Dilithium is presented in the work. The increase in speed is shown in comparison with the reference optimized author 's implementations.

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