A note on the hermite basis computation of large integer matrices

Author(s):  
Ulrich Vollmer
2020 ◽  
Vol 14 ◽  
Author(s):  
Khoirom Motilal Singh ◽  
Laiphrakpam Dolendro Singh ◽  
Themrichon Tuithung

Background: Data which are in the form of text, audio, image and video are used everywhere in our modern scientific world. These data are stored in physical storage, cloud storage and other storage devices. Some of it are very sensitive and requires efficient security while storing as well as in transmitting from the sender to the receiver. Objective: With the increase in data transfer operation, enough space is also required to store these data. Many researchers have been working to develop different encryption schemes, yet there exist many limitations in their works. There is always a need for encryption schemes with smaller cipher data, faster execution time and low computation cost. Methods: A text encryption based on Huffman coding and ElGamal cryptosystem is proposed. Initially, the text data is converted to its corresponding binary bits using Huffman coding. Next, the binary bits are grouped and again converted into large integer values which will be used as the input for the ElGamal cryptosystem. Results: Encryption and Decryption are successfully performed where the data size is reduced using Huffman coding and advance security with the smaller key size is provided by the ElGamal cryptosystem. Conclusion: Simulation results and performance analysis specifies that our encryption algorithm is better than the existing algorithms under consideration.


2020 ◽  
Vol 20 (3) ◽  
pp. 725-737 ◽  
Author(s):  
Zhenping Feng ◽  
Zhuoran Du

AbstractWe consider periodic solutions of the following problem associated with the fractional Laplacian: {(-\partial_{xx})^{s}u(x)+\partial_{u}F(x,u(x))=0} in {\mathbb{R}}. The smooth function {F(x,u)} is periodic about x and is a double-well potential with respect to u with wells at {+1} and -1 for any {x\in\mathbb{R}}. We prove the existence of periodic solutions whose periods are large integer multiples of the period of F about the variable x by using variational methods. An estimate of the energy functional, Hamiltonian identity and Modica-type inequality for periodic solutions are also established.


2001 ◽  
Vol 163 ◽  
pp. 13-53 ◽  
Author(s):  
Jörg Brüdern ◽  
Trevor D. Wooley

We establish that almost all natural numbers not congruent to 5 modulo 9 are the sum of three cubes and a sixth power of natural numbers, and show, moreover, that the number of such representations is almost always of the expected order of magnitude. As a corollary, the number of representations of a large integer as the sum of six cubes and two sixth powers has the expected order of magnitude. Our results depend on a certain seventh moment of cubic Weyl sums restricted to minor arcs, the latest developments in the theory of exponential sums over smooth numbers, and recent technology for controlling the major arcs in the Hardy-Littlewood method, together with the use of a novel quasi-smooth set of integers.


2004 ◽  
Vol 76 (3) ◽  
pp. 303-316 ◽  
Author(s):  
Trevor D. Wooley

AbstractAn asymptotic formula is established for the number of representations of a large integer as the sum of kth powers of natural numbers, in which each representation is counted with a homogeneous weight that de-emphasises the large solutions. Such an asymptotic formula necessarily fails when this weight is excessively light.


Euro ASIC '91 ◽  
1991 ◽  
Author(s):  
G. Hotz ◽  
P. Molitor ◽  
W. Zimmer
Keyword(s):  

2021 ◽  
Author(s):  
Emanuele Vitali ◽  
Davide Gadioli ◽  
Fabrizio Ferrandi ◽  
Gianluca Palermo

2004 ◽  
Vol 18 (2) ◽  
pp. 418-435 ◽  
Author(s):  
Pawel Hitczenko ◽  
Carla D. Savage
Keyword(s):  

2009 ◽  
Vol 138 (4) ◽  
pp. 317-327 ◽  
Author(s):  
P. G. Walsh

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