Encryption/decryption keys can be delivered in a number of ways: person A can select a key and physically deliver it to person B; a third party can select a key and deliver it to both A and B; if they have had previous contact using an encryption, they could use that encryption to send the new code to each other; and lastly, if both A and B have an encrypted connection to a third party, the third party can send the new key over the encrypted connection.
In order to crack RSA, the user could use two separate methods:one is by trying all possible private keys. This can be difficult because the key can be insanely huge. The other approach deals with trying to find the two prime numbers used in the key. If you have the two prime numbers, you can plug it into an algorithm and find the key again. Diffie-Hellman is secure from everything except replay attacks.
Sender ID confirmation is achieved through a number of ways. One is to use your private key to encrypt an entire message to a recipient. When the message is received, the recipient decrypts the message using the sender's public key to encrypt the message. Another way of ID confirmation is to encrypt a small block of bits(the authenticator) with the sender's private key. The recipient will notice that the sender's public key is necessary to decrypt the message.
As for strengths and weaknesses, both RSA and Diffie-Hellman have both. Both are fallible. However difficult to crack, it is possible to decrypt them both. Both have algorithms that, given time, could possibly be broken. Their strengths lie in the complexity of the algorithms. RSA has a variable key length. The longer the message the longer the key. Diffie-Hellman's strength is the difficulty in computing a complex discrete logarithm.
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