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Asked: 2026-06-16T21:59:43+00:00

Let’s say we have a encryption function like this : f(x) = x^5 mod

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Let’s say we have a encryption function like this :

f(x) = x^5 mod 21

How can I get the plain text from the encrypted text which generated by this function? How can I denote the decryption function?

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  1. Editorial Team

    Is this homework? If so, you should tag it homework, and accept answers on some of your past questions.

    This looks like RSA, where the modulus is the product of two primes (i.e. n = p*q). Just follow the steps of the algorithm.In this case, n = 21 = 7*3. This tells you phi(n) = (6*2) = 12.

    If 5 is the encrypting exponent (e), and phi(n) = 12, then to calculate the decrypting exponent, you need to find d such that e*d = 1 (mod phi(n)). Written another way, e-1 = d (mod phi(n)). You can do this with the PowerMod function in Mathematica: PowerMod[5, -1, 12].

    Once you know the modular inverse, the rest becomes easy:

    c = (m)^5 mod 21

    m = (c)^d mod 21

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