Successive Squaring 28^27 mod 76

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Solve 2827 mod 76 using the Successive Squaring Method

Step 1: Convert our power of 27 to binary notation:

Using our binary calculator, we see that 27 in binary form is 11011
The length of this binary term is 5, so this is how many steps we will take for our algorithm below

Step 2: Construct Successive Squaring Algorithm:

iaa2a2 mod p
  0  282828 mod 76 = 28
  1  28784784 mod 76 = 24
  2  24576576 mod 76 = 44
  3  4419361936 mod 76 = 36
  4  3612961296 mod 76 = 4

Take a look at our binary term with values of 1 in red, this signifies which terms we use for our expansion:
4 x 36 x 24 x 28 = 96768 mod 76 = 20


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