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I am new in the field of cryptanalysis and wonder how the differential cryptanalysis work

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You can check several resources about differential cryptanalysis. But there is a very well-explained tutorial about the topic which you can found at Differential Cryptanalysis. This tutorial uses a simple toy cipher to illustrate the idea, you can practice the attack on this toy cipher yourself. You can then read about differential cryptanalysis on Biham's paper

That's not a direct response to your question but I wanted to share these helpful resources as they helped me a lot.

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