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RSA Private Exponent Definition

My question is about signing the RSA.

In case of RSA signing:

encryption → y = x ^ d mod n, decryption → x = y ^ e mod n

  • x → original message
  • y → encrypted message
  • n → module (1024 bits)
  • e → public exhibitor
  • d → private exponent

I know x, y, n and e. Knowing this, can I determine d?

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If you can specify n = p * q, then d * e & equiv; 1 (mod m), where m =? Phi; (n) = (p-1) * (q-1), (? (m) Euler totient function ), in this case you can use the advanced Euclidean algorithm to determine d from e. (d * e - k * m = 1 for some k)

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, , , , n.

:

x = y e mod n = (x d) e mod n = x de mod n = x k & phi; (n) +1 mod n = x * (x & phi; (n)) k mod n = x mod n

(x & phi; (n)) k= 1 mod n - .

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. , - n. -, - mickey x.

472 473 . , . , x, -, d ( ).

There are several ways to do this, all involving x hashing, allowing you to determine the hash in predictable ways to remove some unwanted properties and then sign the value. Recommended methods for this are called “indentation”, although there is one very different method that is not taken into account as the filling method, which can be found in Practical Cryptography.

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