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How to find out the method used to encrypt the string 123456 which results in the value: 6g9SkDLIKa8l2VhafFnHvg==?

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You need to know Key, IV, Padding and Operation Mode. Then you have to try all possible algorithms. Without that (most likely very secret) information (Key, IV, Padding and Operation Mode) this is even more complex and hard to achieve than a know-plaintext attack. To sum it up: its impossible.

EDIT: As said, you can close the possibilities in. But you will not get any farther than a rugh idea of what cipher it is: Is it possible to derive the encryption method from encrypted text?

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