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)

(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]

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Noun

exponentiation - the process of raising a quantity to some assigned power

involution

mathematical 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"

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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.

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The exponentiation is optimized as explained in this section.

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Since modulo operations are much more efficient than exponential operations, only the overhead of the exponentiation operation is considered.

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[T.sub.e] = the running time of one modular exponentiation.

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The pairing cost is much more than the exponentiation and multiplication.

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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.

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Although, there was no immediate claim of responsibility but there is might be some covert hand interested in exponentiation of insecurity in Afghanistan.

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Such advanced algorithms comprise of modular arithmetic, modular exponentiation, prime number theory, Chinese Reminder Theorem, and Fermat's Little Theorem and Euler's Theorem.

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Mccurley et al., "Fast exponentiation with precomputation," in Proceedings of the Eurocrypt on Advances in Cryptology, vol.

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In [24] it was further noted that if one assumes that in this weak-field approximation higher order corrections just lead to an exponentiation