Don't know what exactly you are looking for and if the following is helpful.
The paper is about building a decentralized oracle network to solve problems concerning communication of smart contracts with the outside world (outside the blockchain). This draws some security issues (authenticity, integrity, confidentiality). This one is a formalisation of the requirements for authenticity.
Read the definition on the previous page (p.24) it is written there whtat it means. Basically: The oracle is authentic, if the probability that an adversary can convince a verifier for a wrong message is negligible.
Some of the non-selfexplaining symbols:
[math] pk_i [/math] : public keys
[math] \sigma_{att}[/math] : Actual signature (don't know what 'att' means, from context probably attached)
[math] \mathcal{A}^{\mathcal{F}_{}sgx}(1^{\lambda}) [/math] : Poly-time adversary with access to the trusted hardware functionality SGX
[math] \Sigma [/math]: Is a signature-scheme with [math] \textbf{Sign}[/math] and [math] \textbf{Verify}[/math] functions
[math] \text{prog}_\text{encl}.\text{Resume(id,params)} [/math]: is a [math] \textbf{url}[/math] in their model.
>Is it bullshit nonsense or actually something profound?
It's not bullshit. Tbh, I've not read the whole paper yet, just the first three sections (but plan to, smart contracts are a very interesting topic and what I've read so far was also interesting). But I got the impression (of course I might be wrong on that) that they just wrote this down to have a "cool" math formula in their paper. So I would say not needed but also not bullshit nonsense.
