I'm looking to renew an SSL (okay, TLS) wildcard certificate with a well-known service. I need to provide a CSR, which I have created using a 2048-bit key. I also need to choose a signature hash. The service offers three choices:
SHA-512. Of these,
SHA-256 is the default.
This confuses me. Isn't a longer hash presumed to be always stronger? Is there a good reason I might want the smaller 256-bit signature hash over the larger 512 or is this likely just a UI mistake? Are there some applications that can't use 512 bit hashes yet?