On the equivalence of two ideals in an algebraic field of order 𝑛

1966 ◽  
pp. 114-126
Author(s):  
K. K. Billevič
Keyword(s):  
Algebraic Field

scholarly journals Localization in algebraic field theory

1982 ◽  
Vol 85 (1) ◽  
pp. 87-98 ◽  
Author(s):  
John E. Roberts
Keyword(s):  
Field Theory ◽  
Algebraic Field

A method for determining the canonical basis of an ideal in an algebraic field

1931 ◽  
Vol 105 (1) ◽  
pp. 663-665 ◽  
Author(s):  
C. C. MacDuffee
Keyword(s):  
Canonical Basis ◽  
Algebraic Field

scholarly journals Ordinary reduction of K3 surfaces

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Fedor Bogomolov ◽  
Yuri Zarhin
Keyword(s):  
Number Field ◽  
Field Extension ◽  
K3 Surfaces ◽  
K3 Surface ◽  
Zero Set ◽  
Algebraic Field ◽  
Density Zero ◽  
Archimedean Place ◽  
Ordinary Reduction

AbstractLet X be a K3 surface over a number field K. We prove that there exists a finite algebraic field extension E/K such that X has ordinary reduction at every non-archimedean place of E outside a density zero set of places.

scholarly journals On the exceptional group of a Weierstrass curve in an algebraic field

1954 ◽  
Vol 91 (0) ◽  
pp. 113-142 ◽  
Author(s):  
Gösta Bergman
Keyword(s):  
Exceptional Group ◽  
Algebraic Field

scholarly journals The norm function of an algebraic field extension

1953 ◽  
Vol 3 (1) ◽  
pp. 103-113 ◽  
Author(s):  
Harley Flanders
Keyword(s):  
Field Extension ◽  
Algebraic Field

scholarly journals Jónssonω0-generated algebraic field extensions

1987 ◽  
Vol 128 (1) ◽  
pp. 81-116 ◽  
Author(s):  
Robert Gilmer ◽  
William Heinzer
Keyword(s):  
Algebraic Field ◽  
Field Extensions

scholarly journals Analysis of the complexity of attacks on multivariate cryptographic transformations using algebraic field structure

Radiotekhnika ◽  
2021 ◽  
pp. 59-65
Author(s):  
S.O. Kandiy ◽  
G.A. Maleeva
Keyword(s):  
Comprehensive Analysis ◽  
Field Structure ◽  
Quantum Computers ◽  
Signature Scheme ◽  
Algebraic Field ◽  
Signature Schemes ◽  
Electronic Signature ◽  
World Community ◽  
Private Key ◽  
Standardization Process

In recent years, interest in cryptosystems based on multidimensional quadratic transformations (MQ transformations) has grown significantly. This is primarily due to the NIST PQC competition [1] and the need for practical electronic signature schemes that are resistant to attacks on quantum computers. Despite the fact that the world community has done a lot of work on cryptanalysis of the presented schemes, many issues need further clarification. NIST specialists are very cautious about the standardization process and urge cryptologists [4] in the next 3 years to conduct a comprehensive analysis of the finalists of the NIST PQC competition before their standardization. One of the finalists is the Rainbow electronic signature scheme [2]. It is a generalization of the UOV (Unbalanced Oil and Vinegar) scheme [3]. Recently, another generalization of this scheme – LUOV (Lifted UOV) [5] was found to attack [6], which in polynomial time is able to recover completely the private key. The peculiarity of this attack is the use of the algebraic structure of the field over which the MQ transformation is given. This line of attack has emerged recently and it is still unclear whether it is possible to use the field structure in the Rainbow scheme. The aim of this work is to systematize the techniques used in attacks using the algebraic field structure for UOV-based cryptosystems and to analyze the obstacles for their generalization to the Rainbow scheme.

scholarly journals Coloring Operads for Algebraic Field Theory

2019 ◽  
Vol 67 (8-9) ◽  
pp. 1910004
Author(s):  
Simen Bruinsma
Keyword(s):  
Field Theory ◽  
Algebraic Field
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