A digital signature, if I understand correctly, means sending a message in a clear form along with a message hash, which is encrypted using a private key.
The recipient of the message calculates the hash, decrypts the received hash with the public key, then compares the two hashes to match.
How safe is it? I mean, you can easily get the hash of the message, and you also have an encrypted hash. How to easily find the private key used to create Encrypted_hash?
Example:
Message Hash Encrypted_hash
-----------------------------------------
Hello world! 1234 abcd
Hi there 5678 xyzt
Bla bla 0987 gsdj
...
Given the values of Hash and Encrypted_hash and a sufficient number of these messages, how easy / difficult is it to detect the private key?