Abstract
In addition to the calculational rules for addition, subtraction, and multiplication in residue classes we can also define an operation of exponentiation, where the exponent specifies how many times the base is to be multiplied by itself. Exponentiation is carried out, as usual, by means of recursive calls to multiplication: For a in ℤ m we have a0:= ī and ae+1 := a · ae.
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For a long time on that spot I stood,
Where two roads converged in the wood and I thought:
“Someone going the other way
Might someday stop here for the sake
Of deciding which path to take.”
But my direction lay where it lay.
And walking on, I felt a sense
Of wonder at that difference.
—Ilya Bernstein, Attention and Man
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© 2013 Michael Welschenbach
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Welschenbach, M. (2013). Where All Roads Meet: Modular Exponentiation. In: Cryptography in C and C++. Apress, Berkeley, CA. https://doi.org/10.1007/978-1-4302-5099-9_6
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DOI: https://doi.org/10.1007/978-1-4302-5099-9_6
Publisher Name: Apress, Berkeley, CA
Print ISBN: 978-1-4302-5098-2
Online ISBN: 978-1-4302-5099-9
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