Enter Modular Exponentiation Solve 1113 mod 53 using:
Modular exponentiation
Build an algorithm: n is our exponent = 13
y = 1 and u ≡ 11 mod 53 = 11
See here
n = 13 is odd Since 13 is odd, calculate (y)(u) mod p
(y)(u) mod p = (1)(11) mod 53
(y)(u) mod p = 11 mod 53
11 mod 53 = 11 Reset y to this value
Determine u2 mod p u2 mod p = 112 mod 53
u2 mod p = 121 mod 53
121 mod 53 = 15 Reset u to this value
Cut n in half and take the integer 13 ÷ 2 = 6
n = 6 is even Since 6 is even, we keep y = 11
Determine u2 mod p u2 mod p = 152 mod 53
u2 mod p = 225 mod 53
225 mod 53 = 13 Reset u to this value
Cut n in half and take the integer 6 ÷ 2 = 3
n = 3 is odd Since 3 is odd, calculate (y)(u) mod p
(y)(u) mod p = (11)(13) mod 53
(y)(u) mod p = 143 mod 53
143 mod 53 = 37 Reset y to this value
Determine u2 mod p u2 mod p = 132 mod 53
u2 mod p = 169 mod 53
169 mod 53 = 10 Reset u to this value
Cut n in half and take the integer 3 ÷ 2 = 1
n = 1 is odd Since 1 is odd, calculate (y)(u) mod p
(y)(u) mod p = (37)(10) mod 53
(y)(u) mod p = 370 mod 53
370 mod 53 = 52 Reset y to this value
Determine u2 mod p u2 mod p = 102 mod 53
u2 mod p = 100 mod 53
100 mod 53 = 47 Reset u to this value
Cut n in half and take the integer 1 ÷ 2 = 0
Because n = 0, we stop We have our answer
Final Answer 1113 mod 53 ≡ 52
You have 2 free calculationss remaining
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 a
2 mod p
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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
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