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Welcome to the Monastery.

"... I wouldn't have had a clue what module to install ..."

For future reference, your best sources for this type of information are files with names like README and INSTALL in the distribution.

...
* libssl-dev for OpenSSL on Debian and Ubuntu;
...
* zlib1g-dev on Debian and Ubuntu;
...
[download]

The main module documentation may also help; however, in this case, the "Net::SSLeay - INSTALLATION" section just points you to the README.

— Ken

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