Is there a difference in the security provided by a One Time signature vs a Many time Signature or a Few time signature? Or are they all just different ways of providing the same service?
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The question is quite broad, but the main difference in well designed schemes should be that an OTS can be used once, FTS can be used a few times, and MTS can be used many times.
As an example, with SPHINCS+ you can sign up to $2^{64}$ messages before any degradation in security.
The goal of an FTS scheme (created from an OTS) isn't to add security but to allow one public key to sign a few messages. Similarly for a MTS scheme (built from OTS and/or FTS), to sign many messages.
That is not to say there is not any difference in security. It is difficult to answer generally. An MTS scheme built in a stateless way from a combination of OTS and FTS is really it's own beast. Although it's security will obviously rely on the underlying schemes and how they are used.
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2$\begingroup$ Being able to safely sign multiple messages can definitely be seen as adding security (at least when the scheme is also stateless). OTS are extremely fragile to use because you need to make damn sure never to lose state. $\endgroup$– MaeherCommented Dec 13, 2020 at 8:31