# exponentiation

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## ex·po·nen·ti·a·tion

(ĕk′spə-nĕn′shē-ā′shən)
n. Mathematics
The act of raising a quantity to a power.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## exponentiation

(ˌɛkspəˌnɛnʃɪˈeɪʃən)
n
(in a mathematical equation) the use of an exponent to raise the value of the base number to a power
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## ex•po•nen•ti•a•tion

(ˌɛk spəˌnɛn ʃiˈeɪ ʃən)

n.
the raising of a number to any given power.
[1900–05]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 exponentiation - the process of raising a quantity to some assigned powerinvolutionmathematical operation, mathematical process, operation - (mathematics) calculation by mathematical methods; "the problems at the end of the chapter demonstrated the mathematical processes involved in the derivation"; "they were learning the basic operations of arithmetic"
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
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Notations used in the comparison Notations Descriptions [T.sub.B] Running time of a pairing operation [T.sub.E] Running time of an exponentiation operation in [G.sub.1] [T.sub.M1] Running time of a multiplication in [G.sub.1] [T.sub.M2] Running time of a multiplication in [G.sub.2] |[G.sub.1]| Length of an element in [G.sub.1] |[Z*.sub.p]| Length of an integer in [Z*.sub.p] Table 2.
The exponentiation is optimized as explained in this section.
Since modulo operations are much more efficient than exponential operations, only the overhead of the exponentiation operation is considered.
The pairing cost is much more than the exponentiation and multiplication.
* In order to exchange message, each user has to compute two scalar multiplications, exponentiation, hash function and summation.
The twelve selections that make up the main body of the text are devoted to pairing-based cryptography, parity-friendly elliptical curves, the arithmetic of finite fields, scalar multiplication and exponentiation in pairing groups, final exponentiation, hashing into elliptic curves, and a wide variety of other related subjects.
Although, there was no immediate claim of responsibility but there is might be some covert hand interested in exponentiation of insecurity in Afghanistan.
Such advanced algorithms comprise of modular arithmetic, modular exponentiation, prime number theory, Chinese Reminder Theorem, and Fermat's Little Theorem and Euler's Theorem.
Mccurley et al., "Fast exponentiation with precomputation," in Proceedings of the Eurocrypt on Advances in Cryptology, vol.
In  it was further noted that if one assumes that in this weak-field approximation higher order corrections just lead to an exponentiation
"E" denotes the exponentiation. "0" means matrix-vector multiplication, not exponentiation operation.

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