A Wiener-type attack on an RSA-like cryptosystem constructed from cubic Pell equations

2021 ◽  
Author(s):  
Willy Susilo ◽  
Joseph Tonien
Keyword(s):  
Pell Equations ◽  
Wiener Type

scholarly journals A Boundary Estimate for Singular Sub-Critical Parabolic Equations

2020 ◽  
Author(s):  
Ugo Gianazza ◽  
Naian Liao
Keyword(s):  
Modulus Of Continuity ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Boundary Point ◽  
Cylindrical Domain ◽  
Boundary Estimate ◽  
Critical Range ◽  
Type Integral ◽  
Wiener Type ◽  
Singular Parabolic Equations

Abstract We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-Laplacian type, with $p$ in the sub-critical range $\big(1,\frac{2N}{N+1}\big]$. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.

Expansion theorems of Paley-Wiener type

1947 ◽  
Vol 14 (4) ◽  
pp. 975-978 ◽  
Author(s):  
B�la de Sz. Nagy
Keyword(s):  
Wiener Type

scholarly journals Solution of certain Pell equations

2018 ◽  
Vol 11 (04) ◽  
pp. 1850056 ◽  
Author(s):  
Zahid Raza ◽  
Hafsa Masood Malik
Keyword(s):  
Positive Integer ◽  
Fundamental Solution ◽  
Positive Solutions ◽  
Continued Fraction ◽  
Pell Equation ◽  
Lucas Sequences ◽  
Pell Equations ◽  
Integer Solutions ◽  
Positive Integers

Let [Formula: see text] be any positive integers such that [Formula: see text] and [Formula: see text] is a square free positive integer of the form [Formula: see text] where [Formula: see text] and [Formula: see text] The main focus of this paper is to find the fundamental solution of the equation [Formula: see text] with the help of the continued fraction of [Formula: see text] We also obtain all the positive solutions of the equations [Formula: see text] and [Formula: see text] by means of the Fibonacci and Lucas sequences.Furthermore, in this work, we derive some algebraic relations on the Pell form [Formula: see text] including cycle, proper cycle, reduction and proper automorphism of it. We also determine the integer solutions of the Pell equation [Formula: see text] in terms of [Formula: see text] We extend all the results of the papers [3, 10, 27, 37].

Cubic Pell Equations

2018 ◽  
pp. 205-245
Author(s):  
Samuel A. Hambleton ◽  
Hugh C. Williams
Keyword(s):  
Pell Equations

Generalized Amalgams, With Applications to Fourier Transform

1990 ◽  
Vol 42 (3) ◽  
pp. 395-409 ◽  
Author(s):  
Hans G. Feichtinger
Keyword(s):  
Locally Compact Abelian Group ◽  
Global Behavior ◽  
Local Behavior ◽  
Precise Description ◽  
Locally Compact ◽  
Local Norm ◽  
Survey Article ◽  
Type Spaces ◽  
Wiener Type ◽  
Arbitrary Norms

A recent survey article by J. Fournier and J. Stewart (Bull.AMS 13 (1985), 1-21) explains how amalgams of Lp with lq (as function spaces over any locally compact abelian group G) can be used as an effective tool for the treatment of various problems in harmonic analysis. The present article may be seen as a complement to this survey, indicating further advantages that arise if one works with generalized amalgams (introduced in 1980 under the name of Wiener-type spaces by the author [10]). The main difference between amalgams and these more general spaces is the fact that they allow a more precise description of the local behavior of functions (or distributions) by rather arbitrary norms and that the conditions on the global behavior (of the quantity obtained using that chosen local norm) is described in a way that includes both growth and integrability conditions (not only lq-summability).

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