scholarly journals Diagonal reduction algebra and the reflection equation

2017 ◽  
Vol 221 (2) ◽  
pp. 705-729 ◽  
Author(s):  
S. Khoroshkin ◽  
O. Ogievetsky
Keyword(s):  
Reflection Equation ◽  
Diagonal Reduction

scholarly journals Reflection equation algebra in braided geometry

2008 ◽  
Vol 2 (3) ◽  
pp. 162-174
Author(s):  
Dimitri Gurevich ◽  
Pavel Pyatov ◽  
Pavel Saponov
Keyword(s):  
Reflection Equation ◽  
Reflection Equation Algebra

scholarly journals A Noise Study of the PSW Signature Family: Patching DRS with Uniform Distribution †

Information ◽  
2020 ◽  
Vol 11 (3) ◽  
pp. 133
Author(s):  
Arnaud Sipasseuth ◽  
Thomas Plantard ◽  
Willy Susilo
Keyword(s):  
Uniform Distribution ◽  
Random Noise ◽  
Theoretical Framework ◽  
New Method ◽  
Signature Scheme ◽  
Secret Key ◽  
Initial Work ◽  
Dimensional Ball ◽  
Diagonal Reduction

At PKC 2008, Plantard et al. published a theoretical framework for a lattice-based signature scheme, namely Plantard–Susilo–Win (PSW). Recently, after ten years, a new signature scheme dubbed the Diagonal Reduction Signature (DRS) scheme was presented in the National Institute of Standards and Technology (NIST) PQC Standardization as a concrete instantiation of the initial work. Unfortunately, the initial submission was challenged by Yu and Ducas using the structure that is present on the secret key noise. In this paper, we are proposing a new method to generate random noise in the DRS scheme to eliminate the aforementioned attack, and all subsequent potential variants. This involves sampling vectors from the n-dimensional ball with uniform distribution. We also give insight on some underlying properties which affects both security and efficiency on the PSW type schemes and beyond, and hopefully increase the understanding on this family of lattices.

scholarly journals Set-theoretical solutions to the reflection equation associated to the quantum affine algebra of type $\boldsymbol{A^{(1)}_{n-1}}$

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Atsuo Kuniba ◽  
Masato Okado
Keyword(s):  
Type A ◽  
Baxter Equation ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Reflection Equation ◽  
Theoretical Reflection

Abstract A trick to obtain a solution to the set-theoretical reflection equation from a known one to the Yang–Baxter equation is applied to crystals and geometric crystals associated to the quantum affine algebra of type $A^{(1)}_{n-1}$.

scholarly journals Quantum Weyl algebras and reflection equation algebras at a root of unity

2020 ◽  
Vol 224 (12) ◽  
pp. 106440
Author(s):  
Nicholas Cooney ◽  
Iordan Ganev ◽  
David Jordan
Keyword(s):  
Reflection Equation ◽  
Weyl Algebras ◽  
Root Of Unity
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