# Calculate number of required pairs for differential cryptanalysis

I am currently doing some study on differential cryptanalysis.

However, I have two open questions in the field.

The first question is: How can I calculate the number of messages necessary for a successful attack?

I have read that if you have found a concrete characteristic by the cipher with probability $$p$$ that the number depends directly on $$p$$, which is understandable. However, I don't know how to calculate the number and more importantly, I can't find any literature (book or paper). If someone has a concrete tip, I would like to read it.

My second question is: Is there a measure for evaluating a probability $$p$$ of a characteristic? How high (or good) should a probability be for the attack to be successful? Are there any literature recommendations here?

For differential cryptanalysis roughly $$c/p$$ plaintext ciphertext pairs are needed where $$c$$ is a small constant dependent on the cipher.
As for your second question, unless $$p$$ is much larger than about $$2^{-80}$$ there is no practical attack. After all, you need to encrypt at least as many as $$c/p$$ plaintext ciphertext pairs to collect data before you can mount the attack and the quantity $$c/p$$ is a lower bound on at least your time complexity (possibly also your memory complexity depending on your attack).
However a $$p$$ value that is appreciably larger than $$2^{-k}$$ where $$k$$ is the keylength of the block cipher indicates a weakness in that the cipher is weaker than expected, as in Biham and Shamir's attack on DES.