Conversion from Conventional to Negative-Base Number Representation

1961 ◽  
Vol EC-10 (4) ◽  
pp. 779-779 ◽  
Author(s):  
Louis B. Wadel
Keyword(s):  
Base Number ◽  
Number Representation ◽  
Negative Base

Negative Base Number Systems

1957 ◽  
Vol EC-6 (2) ◽  
pp. 123-123 ◽  
Author(s):  
Louis B. Wadel
Keyword(s):  
Base Number ◽  
Number Systems ◽  
Negative Base

scholarly journals An Efficient Tate Pairing Algorithm for a Decentralized Key-Policy Attribute Based Encryption Scheme in Cloud Environments

Cryptography ◽  
2018 ◽  
Vol 2 (3) ◽  
pp. 14
Author(s):  
Balaji Chandrasekaran ◽  
Ramadoss Balakrishnan
Keyword(s):  
Computational Complexity ◽  
Bilinear Pairing ◽  
Base Number ◽  
Number Representation ◽  
Tate Pairing ◽  
User Privacy ◽  
Attribute Based Encryption ◽  
Key Policy ◽  
Cloud Environments ◽  
The Cost

Attribute-based encryption (ABE) is used for achieving data confidentiality and access control in cloud environments. Most often ABE schemes are constructed using bilinear pairing which has a higher computational complexity, making algorithms inefficient to some extent. The motivation of this paper is on achieving user privacy during the interaction with attribute authorities by improving the efficiency of ABE schemes in terms of computational complexity. As a result the aim of this paper is two-fold; firstly, to propose an efficient Tate pairing algorithm based on multi-base number representation system using point halving (TP-MBNR-PH) with bases 1/2, 3, and 5 to reduce the cost of bilinear pairing operations and, secondly, the TP-MBNR-PH algorithm is applied in decentralized KP-ABE to compare its computational costs for encryption and decryption with existing schemes.

scholarly journals Local Negative Base Transform and Image Scrambling

2018 ◽  
Vol 2018 ◽  
pp. 1-18
Author(s):  
Gangqiang Xiong ◽  
Shengqian Zheng ◽  
Jiang Wang ◽  
Zhanchuan Cai ◽  
Dongxu Qi
Keyword(s):  
Image Encryption ◽  
Information Hiding ◽  
Number Representation ◽  
Arnold Transform ◽  
One Dimensional ◽  
Two Dimensional Image ◽  
New Class ◽  
Inverse Transform ◽  
Negative Base ◽  
Gray Values

Scrambling transform is an important tool for image encryption and hiding. A new class of scrambling algorithms is obtained by exploiting negative integer as the base of number representation to express the natural numbers. Unlike Arnold transform, the proposed scrambling transform is one-dimensional and nonlinear, and an image can be shuffled by using the proposed transform to rearrange the rows and columns of the image separately or to permute the pixels of the image after scanned into a sequence of pixels; it can be also applied to shuffle certain part region of an image. Firstly, the transformation algorithm for converting nonnegative integers in base B to the corresponding integers in base -B is given in this paper, which is the computational core of scrambling transform and the basis of studying scrambling transform. Then, the three kinds of transforms are introduced, that is, negative base transform (abbreviated as NBT), modular negative base transform (MNBT), and local negative base transform (LNBT) with three parameters, where NBT is an injection and MNBT a surjection and LNBT a bijection. The minimum transform periods of LNBT are calculated for some different values of the three parameters, and the algorithm for calculating the inverse transform of LNBT is given. The image scrambled by LBNT can be recovered by the transform period or the inverse transform. Numerical experiments show that LNBT is an efficient scrambling transform and a strong operation of confusing gray values of pixels in the application of image encryption. Therefore, the proposed transform is a novel tool for information hiding and encryption of two-dimensional image and one-dimensional audio.

scholarly journals Confluent Parry numbers, their spectra, and integers in positive- and negative-base number systems

2015 ◽  
Vol 27 (3) ◽  
pp. 745-768 ◽  
Author(s):  
Daniel Dombek ◽  
Zuzana Masáková ◽  
Tomáš Vávra
Keyword(s):  
Base Number ◽  
Number Systems ◽  
Negative Base

An arithmetical-training regime improves number representation and broad mathematical performance

2010 ◽  
Author(s):  
Arava Y. Kallai ◽  
Andrea L. Ponting ◽  
Christian D. Schunn ◽  
Julie A. Fiez
Keyword(s):  
Number Representation ◽  
Mathematical Performance

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Neural Underpinnings of Numerical and Spatial Cognition: An fMRI Meta-Analysis of Brain Regions Associated with Symbolic Number, Arithmetic, and Mental Rotation

2019 ◽  
Author(s):  
Zachary Hawes ◽  
H Moriah Sokolowski ◽  
Chuka Bosah Ononye ◽  
Daniel Ansari
Keyword(s):  
Mental Rotation ◽  
Parietal Lobe ◽  
Meta Analysis ◽  
Likelihood Estimation ◽  
Brain Regions ◽  
Angular Gyrus ◽  
Number Representation ◽  
Neural Underpinnings ◽  
The Right ◽  
Symbolic Number

Where and under what conditions do spatial and numerical skills converge and diverge in the brain? To address this question, we conducted a meta-analysis of brain regions associated with basic symbolic number processing, arithmetic, and mental rotation. We used Activation Likelihood Estimation (ALE) to construct quantitative meta-analytic maps synthesizing results from 86 neuroimaging papers (~ 30 studies/cognitive process). All three cognitive processes were found to activate bilateral parietal regions in and around the intraparietal sulcus (IPS); a finding consistent with shared processing accounts. Numerical and arithmetic processing were associated with overlap in the left angular gyrus, whereas mental rotation and arithmetic both showed activity in the middle frontal gyri. These patterns suggest regions of cortex potentially more specialized for symbolic number representation and domain-general mental manipulation, respectively. Additionally, arithmetic was associated with unique activity throughout the fronto-parietal network and mental rotation was associated with unique activity in the right superior parietal lobe. Overall, these results provide new insights into the intersection of numerical and spatial thought in the human brain.

The Development of the Mental Representation of Numbers 0-10 in Elementary School Children

2020 ◽  
Author(s):  
Anat Feldman ◽  
Michael Shmueli ◽  
Dror Dotan ◽  
Joseph Tzelgov ◽  
Andrea Berger
Keyword(s):  
Sixth Grade ◽  
Number Line ◽  
Number Representation ◽  
Large Numbers ◽  
Position Task ◽  
Sigmoidal Curve ◽  
Anchor Points ◽  
The Right ◽  
Line P ◽  
Best Fit

In recent years, there has been growing interest in the development of mental number line (MNL) representation examined using a number-to-position task. In the present study, we investigated the development of number representation on a 0-10 number line using a computerized version of the number-to-position task on a touchscreen, with restricted response time; 181 children from first through sixth grade were tested. We found that the pattern of estimated number position on the physical number line was best fit by the sigmoidal curve function–which was characterized by underestimation of small numbers and overestimation of large numbers–and that the breakpoint changed with age. Moreover, we found that significant developmental leaps in MNL representation occurred between the first and second grades and again between the second and third grades, which was reflected in the establishment of the right endpoint and the number 5 as anchor points, yielding a more accurate placement of other numbers along the number line.

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