Successive Squaring 22^128mod101 Image to Crop

Enter Modular Exponentiation

Solve 22128 mod 101 using:

the Successive Squaring Method

Step 1: Convert our power of 128 to binary notation:

Using our binary calculator, we see that 128 in binary form is 10000000

The length of this binary term is 8, so this is how many steps we will take for our algorithm below

Step 2: Construct Successive Squaring Algorithm:
iaa2a2 mod p
  0  222222 mod 101 = 22
  1  22484484 mod 101 = 80
  2  8064006400 mod 101 = 37
  3  3713691369 mod 101 = 56
  4  5631363136 mod 101 = 5
  5  52525 mod 101 = 25
  6  25625625 mod 101 = 19
  7  19361361 mod 101 = 58

Step 3: Review red entries

Look at the binary term with values of 1 in red

This signifies which terms we use for expansion:

Final Answer

58 = 58 mod 101 = 58

You have 1 free calculations remaining


What is the Answer?

58 = 58 mod 101 = 58

How does the Modular Exponentiation and Successive Squaring Calculator work?

Free Modular Exponentiation and Successive Squaring Calculator - Solves xn mod p using the following methods:
* Modular Exponentiation
* Successive Squaring
This calculator has 1 input.

What 1 formula is used for the Modular Exponentiation and Successive Squaring Calculator?

Successive Squaring I = number of digits in binary form of n. Run this many loops of a2 mod p

For more math formulas, check out our Formula Dossier

What 6 concepts are covered in the Modular Exponentiation and Successive Squaring Calculator?

exponent
The power to raise a number
integer
a whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...
modular exponentiation
the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus)
modulus
the remainder of a division, after one number is divided by another.
a mod b
remainder
The portion of a division operation leftover after dividing two integers
successive squaring
an algorithm to compute in a finite field

Example calculations for the Modular Exponentiation and Successive Squaring Calculator

Modular Exponentiation and Successive Squaring Calculator Video


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