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There are several algorithms, but the most efficient one, called (modular) fast exponentiation, uses a property on the binary writing of $ e $. Writing $ e=\sum_{i=0}^{m-1}a_{i}2^{i} $ over $ m $ bits with $ a_i $ the binary values (0 or 1) in writing in base 2 of $ e $ (with $ a_{m-1} = 1 $)
- RSA Cipher
Method 1: Prime numbers factorization of $ n $ to find $ p $...
- Modular Inverse Calculator
Example: $ 3^{-1} \equiv 4 \mod 11 $ because $ 4 \times 3 =...
- Euclidean Division
In mathematics, the remainder of Euclidean division can be...
- Base 58
Base 58 is an encoding system that converts binary data into...
- Prime Factors Decomposition
Then divide by $ 3 $, $ 147/3 = 49 $ so $ 147 $ is divisible...
- RSA Cipher
3 dni temu · Master modular arithmetic with our power mod calculator, perfect for calculations with exponents. Simplify complex math effortlessly. Try now!
This tool allows you to solve online modular exponentiation step-by-step. The numbers entered must be positive integers except for the base, that may be negative too, and the modulo, that must only be greater than zero.
Free Modulo calculator - find modulo of a division operation between two numbers step by step
Use fast modular exponentiation as described in the next lesson. Right after that lesson there is a calculator for modular exponents, so you can check your calculations.
You have to be careful about what the negative in the exponent means, namely $2^{-1}$ is the element $a$ that satisfies $$ 2a\cong 1\mod 25 $$ With a little thought, this is seen to be $a=13$. Then $$ 2^{-11}=13^{11} $$ which you may compute by finding a pattern.
Our modulo calculator give you value of a MOD b, and works with negative numbers too which some mod calculators do not. Find out more on what MOD is.
