scholarly journals Construction of a polynomial invariant annihilation attack of degree 7 for T-310

Cryptologia ◽  
2020 ◽  
Vol 44 (4) ◽  
pp. 289-314
Author(s):  
Nicolas T. Courtois ◽  
Aidan Patrick ◽  
Matteo Abbondati
Keyword(s):  
Polynomial Invariant

scholarly journals FROM RIBBON CATEGORIES TO GENERALIZED YANG–BAXTER OPERATORS AND LINK INVARIANTS (AFTER KITAEV AND WANG)

2013 ◽  
Vol 24 (01) ◽  
pp. 1250126 ◽  
Author(s):  
SEUNG-MOON HONG
Keyword(s):  
The Other ◽  
Polynomial Invariant ◽  
Link Invariants ◽  
Fusion Categories ◽  
New Family ◽  
Kauffman Polynomial ◽  
Twist Structure

We consider two approaches to isotopy invariants of oriented links: one from ribbon categories and the other from generalized Yang–Baxter (gYB) operators with appropriate enhancements. The gYB-operators we consider are obtained from so-called gYBE objects following a procedure of Kitaev and Wang. We show that the enhancement of these gYB-operators is canonically related to the twist structure in ribbon categories from which the operators are produced. If a gYB-operator is obtained from a ribbon category, it is reasonable to expect that two approaches would result in the same invariant. We prove that indeed the two link invariants are the same after normalizations. As examples, we study a new family of gYB-operators which is obtained from the ribbon fusion categories SO (N)2, where N is an odd integer. These operators are given by 8 × 8 matrices with the parameter N and the link invariants are specializations of the two-variable Kauffman polynomial invariant F.

A Polynomial Invariant of Graphs On Orientable Surfaces

2001 ◽  
Vol 83 (3) ◽  
pp. 513-531 ◽  
Author(s):  
Béla Bollobás ◽  
Oliver Riordan
Keyword(s):  
Polynomial Invariant ◽  
Orientable Surfaces

Entanglement in four qubit states: Polynomial invariant of degree 2, genuine multipartite concurrence and one-tangle

2019 ◽  
Vol 383 (8) ◽  
pp. 707-717 ◽  
Author(s):  
M.A. Jafarizadeh ◽  
M. Yahyavi ◽  
N. Karimi ◽  
A. Heshmati
Keyword(s):  
Polynomial Invariant ◽  
Qubit States

A polynomial invariant of doubly periodic braided structures

2006 ◽  
Vol 32 (5) ◽  
pp. 445-448
Author(s):  
S. A. Grishanov ◽  
V. R. Meshkov ◽  
A. V. Omel’chenko
Keyword(s):  
Polynomial Invariant

A MULTI-VARIABLE POLYNOMIAL INVARIANT FOR UNORIENTED VIRTUAL KNOTS AND LINKS

2009 ◽  
Vol 18 (05) ◽  
pp. 625-649 ◽  
Author(s):  
YASUYUKI MIYAZAWA
Keyword(s):  
Crossing Number ◽  
Weighted Sum ◽  
Virtual Link ◽  
Polynomial Invariant ◽  
Virtual Knots ◽  
Virtual Links ◽  
Knots And Links

We construct a multi-variable polynomial invariant Y for unoriented virtual links as a certain weighted sum of polynomials, which are derived from virtual magnetic graphs with oriented vertices, on oriented virtual links associated with a given virtual link. We show some features of the Y-polynomial including an evaluation of the virtual crossing number of a virtual link.

Direct measurement of the polynomial invariant of degree 2

2021 ◽  
Author(s):  
Marziyeh Yahyavi ◽  
Mohammad Ali Jafarizdeh ◽  
Ahmad Heshmati ◽  
Naser Karimi
Keyword(s):  
Direct Measurement ◽  
Polynomial Invariant

GENERALIZED INDEX POLYNOMIALS FOR VIRTUAL LINKS

2012 ◽  
Vol 21 (14) ◽  
pp. 1250128
Author(s):  
KYEONGHUI LEE ◽  
YOUNG HO IM
Keyword(s):  
Knot Theory ◽  
Recursive Method ◽  
Polynomial Invariant ◽  
Polynomial Invariants ◽  
Virtual Knots ◽  
Virtual Links

We construct some polynomial invariants for virtual links by the recursive method, which are different from the index polynomial invariant defined in [Y. H. Im, K. Lee and S. Y. Lee, Index polynomial invariant of virtual links, J. Knot Theory Ramifications19(5) (2010) 709–725]. We show that these polynomials can distinguish whether virtual knots can be invertible or not although the index polynomial cannot distinguish the invertibility of virtual knots.

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