Enter Modular Exponentiation
Solve 314 mod 23 using:
Modular exponentiation
Build an algorithm:
n is our exponent = 14
y = 1 and u ≡ 3 mod 23 = 3
See here
n = 14 is even
Since 14 is even, we keep y = 1
Determine u2 mod p
u2 mod p = 32 mod 23
u2 mod p = 9 mod 23
9 mod 23 = 9
Reset u to this value
Cut n in half and take the integer
14 ÷ 2 = 7
n = 7 is odd
Since 7 is odd, calculate (y)(u) mod p
(y)(u) mod p = (1)(9) mod 23
(y)(u) mod p = 9 mod 23
9 mod 23 = 9
Reset y to this value
Determine u2 mod p
u2 mod p = 92 mod 23
u2 mod p = 81 mod 23
81 mod 23 = 12
Reset u to this value
Cut n in half and take the integer
7 ÷ 2 = 3
n = 3 is odd
Since 3 is odd, calculate (y)(u) mod p
(y)(u) mod p = (9)(12) mod 23
(y)(u) mod p = 108 mod 23
108 mod 23 = 16
Reset y to this value
Determine u2 mod p
u2 mod p = 122 mod 23
u2 mod p = 144 mod 23
144 mod 23 = 6
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 = (16)(6) mod 23
(y)(u) mod p = 96 mod 23
96 mod 23 = 4
Reset y to this value
Determine u2 mod p
u2 mod p = 62 mod 23
u2 mod p = 36 mod 23
36 mod 23 = 13
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
314 mod 23 ≡ 4
What is the Answer?
314 mod 23 ≡ 4
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 field
Example calculations for the Modular Exponentiation and Successive Squaring Calculator
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