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The paper Snarky signatures: Minimal Signatures of Knowledge from Simulation-Extractable SNARKs by Jens Groth contains this line (on page 16):

$$\eta \in (\mathbb{Z})^{\left|Q\right|} \leftarrow \chi_A(trans_A)$$

What does "$trans_A$" mean? I suspect this is supposed to be the transcript between the attacker and the oracles its given. Is this correct?

I'm not used to this notation. Does it mean "transcript between that thing that I casually noted to it in the end and everything its given somewhere else"?

The notation section says: "For an algorithm A we define $trans_A$ to be a list containing all of A’s inputs and outputs, including random coins." Does this list include a transcript?

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  • $\begingroup$ You ask whether $\mathsf{trans}_\mathcal A$ contains a "transcript"; that question is meaningless because the word "transcript" never appears in the paper. You might as well ask whether it contains a teacup. $\endgroup$
    – fkraiem
    Jul 8, 2019 at 14:31
  • $\begingroup$ In other words, forget the word "transcript"; that word does not exist in the context of this paper. $\mathsf{trans}_\mathcal A$ is exactly what the definition says it is; no more, no less. $\endgroup$
    – fkraiem
    Jul 8, 2019 at 14:39

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On page 5 (section Definitions, subsection Notation) it states:

For an algorithm $A$ we define $\text{trans}_A$ to be a list containing all of A’s inputs and outputs, including random coins.

It's (as far as I can tell) a freely invented and new notation, because after a quick Google-search I found only this book which also contains it and it states Jens Groth as the author there. The book also looks like some sort of collection of cryptographic papers.

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  • $\begingroup$ That same quote is in my question. It's unclear to me what the abbreviation means and whether that data contains a transcript. $\endgroup$
    – UTF-8
    Jul 8, 2019 at 14:04
  • $\begingroup$ The book is (part 2 of) the proceedings of the CRYPTO 2017 conference, which is where the paper was formally published. $\endgroup$
    – fkraiem
    Jul 8, 2019 at 14:32
  • $\begingroup$ @UTF-8 the Definition is pretty clear. The list "contains a transcript" if and only if one of A's inputs or outputs is a transcript. $\endgroup$
    – Maeher
    Jul 8, 2019 at 14:54
  • $\begingroup$ Okay, then I'm probably just having a really hard time how the correct factors for the linear combination in assumption 4.1 can be computed, just with access to the inputs and outputs of the attacker but without access to the oracle transcripts. But I'll wait some time before accepting this answer in case someone comes up with a better solution and also for me to have some time to understand how this magic is supposed to work. $\endgroup$
    – UTF-8
    Jul 8, 2019 at 18:17

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