I'm doing some light and fun reading and I'd like to get some clarification, please.
I know that SSL uses public-key cryptography and is the backbone behind the HTTPS connection. The encryption used in SSL can be AES-128, 256, or whatever. What part of the secure connection does SHA play in security? If the connection is secured, and encrypted with AES, where does SHA come into play?
SHA is a hash function.
Hash functions have nothing to do with encryption. They are used in digital signing and message integrity.
For example in certificates, there is the public key but there is also the hash to ensure that the certificate has not been altered
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