Final answer:
In stream ciphers, if the same key is used to encrypt data more than once, the security is compromised. An attacker could use plaintext attacks to decrypt the data or recover the key stream. The necessity of unique key usage in encryption sessions is critical for maintaining security.
Step-by-step explanation:
If key generation and handling in stream ciphers is not done properly and the same key is used to encrypt data two or more times, option (1) the encrypted data will be the same for each encryption is incorrect. Instead, what happens is that it leads to option (2) the encrypted data will be different for each encryption as a result of the stream cipher combining the key with a pseudorandom key stream. If the same key is used for multiple encryptions, the security can be compromised because if two pieces of data are encrypted with the same key stream, an attacker could potentially use known-plaintext attacks to decrypt the data or recover the key stream.
A critical point to understand in the context of stream ciphers is that the security of a stream cipher greatly depends on using a unique key for each encryption session. Reusing a key can lead to various attacks such as the two-time pad (also known as stream cipher key reuse attack), where the ciphertexts can be combined to cancel out the key stream, leaving a combination of the plaintexts that can often be broken with relative ease, especially if patterns or known plaintext can be found.