If the message number is 64 bits long, then there could be a total of 2^64 possible message numbers. This is because each bit has two possible states (0 or 1) and there are 64 bits in total, so 2 to the power of 64 gives us the total number of possible message numbers.
For the authentication function, a common choice for a secure channel with a security factor of 256 bits would be HMAC-SHA256. This is a type of message authentication code (MAC) that uses a secret key and a cryptographic hash function to provide message integrity and authenticity. HMAC-SHA256 is widely used in secure communication protocols such as TLS and VPNs.
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