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Efficient Multiplication Using Type 2 Optimal Normal Bases [chapter]

Joachim von zur Gathen, Amin Shokrollahi, Jamshid Shokrollahi
2007 Lecture Notes in Computer Science  
In this paper we propose a new structure for multiplication using optimal normal bases of type 2.  ...  Using this technique we can reduce the asymptotic cost of multiplication in optimal normal bases of type 2 from 2M(n) + O(n) reported by Gao et al. (2000) to M(n) + O(n log n) operations in Fq, where M  ...  Applications in cryptography have stimulated research about efficient multiplication using optimal normal bases of type 2.  ... 
doi:10.1007/978-3-540-73074-3_6 fatcat:3a2wgdfphzdgrcbxnnkftjbdwy

An Efficient Algorithm for Computing Inverses in GF(2m) Using Dual Bases [chapter]

Hyeong Seon Yoo, Seok Ung Yoon, Eui Sun Kim
2003 Lecture Notes in Computer Science  
This paper propose a new multiplicative inverse algorithm for Galois field GF(2 n ) whose elements are represented by optimal normal bases type II.  ...  The efficiency of the arithmetic algorithms depends on the basis and many foregoing papers use either polynomial or optimal normal basis.  ...  An Efficient Algorithm for Computing Inverses in GF(2 m ) Using Dual Bases  ... 
doi:10.1007/3-540-44864-0_103 fatcat:fvrgwtunmngt7gkjykmdv575fy

SASqPCR: Robust and Rapid Analysis of RT-qPCR Data in SAS

Daijun Ling, Martin Beer
2012 PLoS ONE  
This program has multiple macros for assessment of PCR efficiencies, validation of reference genes, optimization of data normalizers, normalization of confounding variations across samples, and statistical  ...  Analysis of RT-qPCR data requires many iterative computations for data normalization and analytical optimization.  ...  For examining multiple genes/treatment types, users may consider reporting P values sequentially adjusted using Benjamini and Hochberg False Discovery Rate to correct for multiple comparisons [11] .  ... 
doi:10.1371/journal.pone.0029788 pmid:22238653 pmcid:PMC3253109 fatcat:ufo75kq7ibewzn6dg2h3tlvi2i

Page 428 of IEEE Transactions on Computers Vol. 52, Issue 4 [page]

2003 IEEE Transactions on Computers  
\d type-II optimal normal bases.  ...  428 IEEE TRANSACTIONS ON COMPUTERS, VOL. 52, NO. 4, APRi\ 200 REY alg Efficient Multiplication Beyond | Optimal Normal Bases | 2 2.1 Arash Reyhani-Masoleh, Member, IEEE, and M.  ... 

Efficient Software Implementation for Finite Field Multiplication in Normal Basis [chapter]

Peng Ning, Yiqun Lisa Yin
2001 Lecture Notes in Computer Science  
In this paper, we present new techniques for efficient software implementation of binary field multiplication in normal basis.  ...  Our techniques are more efficient in terms of both speed and memory compared with alternative approaches.  ...  Formula (2) will be useful in later discussions. Multiplication with Optimal Normal Basis An optimal normal basis (ONB) [1, 12] is a normal basis which has the lowest complexity.  ... 
doi:10.1007/3-540-45600-7_21 fatcat:lblnb2vatfh67mxvisatad4awq

An efficient optimal normal basis type II multiplier

B. Sunar, C.K. Koc
2001 IEEE transactions on computers  
AbstractÐThis paper presents a new parallel multiplier for the Galois field qp P m whose elements are represented using the optimal normal basis of type II.  ...  Index TermsÐGalois field, optimal normal basis, Massey-Omura multiplier, space complexity. ae 1. Note that I and I are sets, i.e., the elements are unordered.  ...  These bases are historically named as the optimal normal basis of type I and the optimal normal basis of type II.  ... 
doi:10.1109/12.902754 fatcat:6n2xxca2svcuhlqg66qdqo6btm

Artin–Schreier extensions of normal bases

David Thomson, Colin Weir
2018 Finite Fields and Their Applications  
These new bases are motivated by Artin-Schreier theory, and are particularly useful when creating bases in Artin-Schreier extensions of finite fields.  ...  This manuscript deals with extending a normal basis to a new basis which permits both computationally inexpensive exponentiation and multiplication.  ...  Let F 2 n admit a Type I optimal normal basis B over F 2 .  ... 
doi:10.1016/j.ffa.2018.06.010 fatcat:b25py2wpejhmrpge4h247owdv4

Implementation And Analysis Of Elliptic Curve Cryptosystems Over Polynomial Basis And Onb

Yong-Je Choi, Moo-Seop Kim, Hang-Rok Lee, Ho-Won Kim
2007 Zenodo  
In general, it is said that normal bases, especially optimal normal bases (ONB) which are special cases on normal bases, are efficient for the implementation in hardware in comparison with polynomial bases  ...  Polynomial bases and normal bases are both used for elliptic curve cryptosystems, but field arithmetic operations such as multiplication, inversion and doubling for each basis are implemented by different  ...  Any bases in both can be used for ECCs, however, some special cases such as trinomial bases, pentanomial bases and optimal normal bases (ONBs) are, in practice, used for the purpose of efficient operations  ... 
doi:10.5281/zenodo.1330374 fatcat:ypet7u6pqbfofesgswghjbbj6m

Optimized GF(2k) ONB type I multiplier architecture based on the Massey–Omura multiplication pattern

A P Fournaris, O Koufopavlou
2005 Journal of Physics, Conference Series  
GF(2 k ) Finite Fields defined over Optimal Normal Bases (ONB) can be very advantageous in term of gates number and Multiplication Time Delay.  ...  In this paper, a method for designing Type I Optimal Normal Basis multipliers and an Optimal Normal Basis (ONB) Type I Multiplier Hardware architecture is proposed that, through parallelism and pairing  ...  Especially Multiplication using Normal Basis representation of the GF(2 k ) Finite Field are even more useful when in Optimal form (ONB) .  ... 
doi:10.1088/1742-6596/10/1/093 fatcat:kxugkcfptjgufbvpisffdmzdvy

Optimization of EDM Process Parameters on Titanium Super Alloys Based on the Grey Relational Analysis

J. Laxman,, Dr. K. Guru Raj
2014 International Journal of Engineering Research  
In this paper deals with the optimization of EDM process parameters using the grey relational analysis (GRA) based on an orthogonal array for the multi response process.  ...  The combination of Taguchi method with GRA enables to determine the optimal parameters for multiple response process.  ...  hybrid Metal Matrix composite Lin C.L. et. al presented the grey relational analysis based on orthogonal array and fuzzy based Taguchi method for the optimization of the EDM process with multiple process  ... 
doi:10.17950/ijer/v3s5/513 fatcat:qm45widvkbedfcmoxxs3jbsxfy

An Optimization-Based Approach to Calculate Confidence Interval on Mean Value with Interval Data

Kais Zaman, Saraf Anika Kritee
2014 Journal of Optimization  
In this paper, we present efficient algorithms based on continuous optimization to find the confidence interval on mean values with interval data.  ...  Several sets of interval data with different numbers of intervals and type of overlap are presented to demonstrate the proposed methods.  ...  The most commonly used method for the construction of confidence interval on mean is the standard interval, which is based on an asymptotic normality assumption [16] .  ... 
doi:10.1155/2014/768932 fatcat:k3dz2r6zqzacxkxf2nruxapwcm

Type-based multiple-access with bandwidth extension for the decentralized estimation in wireless sensor networks

Xin Wang, Chenyang Yang
2010 2010 IEEE International Conference on Acoustics, Speech and Signal Processing  
Type-based multiple-access (TBMA) is a bandwidth efficient transmission scheme for decentralized estimation in wireless sensor networks (WSNs) over non-orthogonal multiple-access channels, whereas its  ...  In this paper, we improve its performance in the fading channels by using more resources for transmitting each type, which is named as TBMA with bandwidth extension (TBMA-BE).  ...  Then the type-based multiple-access (TBMA) with quantized observations, which assigns one orthogonal waveform to represent each type, is introduced for the decentralized estimation [2] and detection  ... 
doi:10.1109/icassp.2010.5496158 dblp:conf/icassp/WangY10 fatcat:wakwqsfjuvcsfnieonwek454u4

Determination of Optimum Working Parameters for Multiple Response Characteristics of Worm Gear Box

2019 International journal of recent technology and engineering  
The reason for this task is to optimize the multiple response of single start worm gear using three working parameters to improve its performance.  ...  Taguchi Grey Relational Analysis (GRA) is the method used to determine the influence of type of lubricant, volume of lubricant and speed of worm gear on multiple responses (input torque & lubricant heating  ...  The overall evaluation of the multiple process responses is based on the grey relational grade.  ... 
doi:10.35940/ijrte.c4656.098319 fatcat:ae7z3vszezgcvivjtowwhqntru

An Improvement of Cyclic Vector Multiplication Algorithm

Hidehiro Kato, Yasuyuki Nogami, Tomoki Yoshida, Kenta Nekado, Shoichi Takeuchi, Yoshitaka Morikawa
2008 2008 Third International Conference on Convergence and Hybrid Information Technology  
Since OEF uses Karatsuba-based polynomial multiplication and an irreducible binomial as the modular polynomial, a multiplication in OEF is efficiently carried out.  ...  In the previous work (Kato et al, 2007) , CVMA 344 is quite efficient when m is small such as for the use of pairing-based cryptographic applications.  ...  /books/convergence-and-hybrid-information-technologies/an-improvement-ofcyclic-vector-multiplication-algorithm © 2010 The Author(s).  ... 
doi:10.1109/iccit.2008.166 fatcat:mgnecnz6jzfuxgxyg3idrbjxty

Non-orthogonal binary subspace and its applications in computer vision

Hai Tao, R. Crabb, Feng Tang
2005 Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1  
We investigate the optimized orthogonal matching pursuit method for finding the best NBS base vectors.  ...  These base vectors possess the property that the inner product operation with them can be computed very efficiently.  ...  To achieve this, the OOMP algorithm is performed to obtain the optimal base vectors. Then, the numerator is computed using Eq. (11) (12) , with | | Λ multiplications and 1 | | 4 − Λ additions.  ... 
doi:10.1109/iccv.2005.169 dblp:conf/iccv/TaoCT05 fatcat:ntw42mj2lrbmrcc5weaw4iasom
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