Successive Squaring 22^128mod101 
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:
| i | a | a2 | a2 mod p | | 0 | 22 | 22 | 22 mod 101 = 22 |
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| 1 | 22 | 484 | 484 mod 101 = 80 |
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| 2 | 80 | 6400 | 6400 mod 101 = 37 |
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| 3 | 37 | 1369 | 1369 mod 101 = 56 |
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| 4 | 56 | 3136 | 3136 mod 101 = 5 |
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| 5 | 5 | 25 | 25 mod 101 = 25 |
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| 6 | 25 | 625 | 625 mod 101 = 19 |
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| 7 | 19 | 361 | 361 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 pFor more math formulas, check out our Formula Dossier
What 6 concepts are covered in the Modular Exponentiation and Successive Squaring Calculator?
exponentThe power to raise a numberintegera whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...modular exponentiationthe remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus)modulusthe remainder of a division, after one number is divided by another.
a mod bremainderThe portion of a division operation leftover after dividing two integerssuccessive squaringan algorithm to compute in a finite fieldExample calculations for the Modular Exponentiation and Successive Squaring Calculator
Modular Exponentiation and Successive Squaring Calculator Video
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