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I've written a Lua binding to the bn subsystem of OpenSSL:

This is a fast, integer-only, big-number library that is suitable for
number-theoretical and cryptographic applications.

If you're running Unix, you probably already have OpenSSL installed,
and so you only need to do "make".

I thank Valerio Schiavoni for telling me about the existence of bn.

Checksum and other data available at

Like all my code, lbn is in the public domain.
Enjoy. All feedback welcome.