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Is Bitcoin’s supply inflated by the exchanges of Bitcoin?

For example, would an exchange of Bitcoin hold accounts for 100,000 customers, and they collective have 8000 bitcoins, but the exchange itself does not hold 8000 bitcoin, but only 1600 for customers to redeem (to transfer to their own wallet if they want to), and therefore, inflating the bitcoin supply by 6400 bitcoins?

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Open source cryptographic library with permissive enough licence

This seems to be a little bit contradictory, but in the frame of a project, i need to provide digital signature verification. The software will be proprietary, except the digital signature verification process may be open source. Like, the developers can create everything from scratch, but obviously, cryptographic library is difficult (and pointless!) to replace.::Listen

This seems to be a little bit contradictory, but in the frame of a project, i need to provide digital signature verification.

The software will be proprietary, except the digital signature verification process may be open source. Like, the developers can create everything from scratch, but obviously, cryptographic library is difficult (and pointless!) to replace.

Intent is to rely on an Open Source cryptographic library such as OpenSSL, LibreSSl, GNUTLS… which may fulfill this purpose of digital signature verification.

However, the end user will not have access to the information that product embeds a digital signature and which library is used to provide this signature verification.

Does one of this library (or one another) be permissive enough in order to let this digital signature verification being implemented, without implying that overall code and binary getting Open Source, and without implying that end user shall be notified of the cryptographic library being used ?

Thanks for your answers, (do not hesitate to move in a more appropriate stackexchange community if any).