I am working on a python decryption code using an encryption code that is already available.

In the encryption code, I have X = pow(a,b,c) I know X, a, c. How can I know value b?

CodePudding user response：

Assuming that

• a is the base,
• b is the power, and
• c is the mod c-part in a^b mod c,

then computing b given a, c and a^b mod c would be the discrete logarithm problem, which is practically intractable for the cases you'd be usually interested in when dealing with cryptographic algorithms.

CodePudding user response：

You can't, that's the point. pow(a,b,c) is a ** b modulo c, where modulo means the remainder in an integer division by c. For example, pow(4, 3, 5) is 4 ** 3 modulo 5, which is 4 (4 ** 3 is 64, modulo 5 is 4 because that's the remainder of 60:5).

But you also get 4 as a result of, for example, pow(4, 1, 5) (because 4 ** 1 = 4, giving a remainder of 4).

So the bottom line is: You can't unambiguously derive b from having X, a and c in your equation because there are multiple bs that will fulfil the equation. That's one of the reasons why asymmetric encryption likes to use the modulo function.