Web Reference: How can we calculate A^B mod C quickly if B is a power of 2 ? Using modular multiplication rules: i.e. A^2 mod C = (A * A) mod C = ((A mod C) * (A mod C)) mod C. We can use this to calculate 7^256 mod 13 quickly. We can substitute our previous result for 7^1 mod 13 into this equation. Feb 5, 2026 · Start with the result as 1. Use a loop that runs while the exponent n is greater than 0. If the current exponent is odd, multiply the result by the current base and apply the modulo. Square the base and take the modulo to keep the value within bounds. Divide the exponent by 2 (ignore the remainder). Repeat the process until the exponent becomes 0. Recall when we first encountered modular inversion we argued we could try every element in turn to find an inverse, but this was too slow to be used in practice.
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