Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
A Novel RSA Attack Leveraging Christoffel and Stern-Brocot Tree Properties
View through CrossRef
Abstract
This research paper explores the properties of ChristoffelWords, which are formed using a binary alphabet. These words have been extensively studied by Jean Berstel, Christophe Reutenauer, and others, due to their intriguing combinatorial and geometrical characteristics. We have established specific combinatorial properties of the Christoffel and Stern-Brocot trees, which in certain cases can be effectively utilized to compute the modulo multiplicative inverse of a natural number and have also presented a novel algorithm to attack the RSA cryptosystem using this application.
Title: A Novel RSA Attack Leveraging Christoffel and Stern-Brocot Tree Properties
Description:
Abstract
This research paper explores the properties of ChristoffelWords, which are formed using a binary alphabet.
These words have been extensively studied by Jean Berstel, Christophe Reutenauer, and others, due to their intriguing combinatorial and geometrical characteristics.
We have established specific combinatorial properties of the Christoffel and Stern-Brocot trees, which in certain cases can be effectively utilized to compute the modulo multiplicative inverse of a natural number and have also presented a novel algorithm to attack the RSA cryptosystem using this application.
Related Results
Stern–Brocot Tree
Stern–Brocot Tree
Christoffel words have a strong connection with continued fractions of rational numbers, as was recognized by Christoffel. They are in some sense equivalent to them, being a way to...
From Christoffel Words to Markoff Numbers
From Christoffel Words to Markoff Numbers
Christoffel introduced in 1875 a special class of words on a binary alphabet, linked to continued fractions. Some years laterMarkoff published his famous theory, called nowMarkoff ...
Advancing Interceptor Design: Analyzing the Impact of Extended Stern Form on Deep-V Planing Hulls
Advancing Interceptor Design: Analyzing the Impact of Extended Stern Form on Deep-V Planing Hulls
The deep-v planing hull is designed to operate at high speeds because most of the hull’s weight is supported by the hydrodynamic lift acting on the hull base. Planing hull form cha...
Monitoring the Attack Incidences and Damage Caused by the Almond Bark Beetle, Scolytus amygdali, in Almond Orchards
Monitoring the Attack Incidences and Damage Caused by the Almond Bark Beetle, Scolytus amygdali, in Almond Orchards
The almond bark beetle, Scolytus amygdali Geurin-Meneville, is responsible for significant loss of fruit production in almond orchards throughout the world. Here, we studied the da...
Postoperative Opioid Dependence in Patients Undergoing Either Total or Reverse Shoulder Arthroplasty for Proximal Humerus Fracture Fixation
Postoperative Opioid Dependence in Patients Undergoing Either Total or Reverse Shoulder Arthroplasty for Proximal Humerus Fracture Fixation
Introduction: In elderly patients who have proximal humerus fractures, treatment commonly involves total shoulder arthroplasty (TSA) or reverse shoulder arthroplasty (RSA). Followi...
El árbol de Stern-Brocot
El árbol de Stern-Brocot
En el presente artículo se narra una conversación imaginaria entre la autora y su imaginario tío Pedro. El tema de esta conversación es la construcción de un árbol binario a partir...
The Sensitivity Feature Analysis for Tree Species Based on Image Statistical Properties
The Sensitivity Feature Analysis for Tree Species Based on Image Statistical Properties
While the statistical properties of images are vital in forestry engineering, the usefulness of these properties in various forestry tasks may vary, and certain image properties mi...
Inter-specific variations in tree stem methane and nitrous oxide exchanges in a tropical rainforest
Inter-specific variations in tree stem methane and nitrous oxide exchanges in a tropical rainforest
<p>Tropical forests are the most productive terrestrial ecosystems, global centres of biodiversity and important participants in the global carbon and water cycles. T...