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Document known issue with security argument
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emlun committed Jan 29, 2025
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Expand Up @@ -292,6 +292,22 @@ can also be used to also defeat the msKS property of pqARKG.
Thus we conclude that pqARKG-H retains the msKS property of pqARKG.


## Known issues

We are not ourselves convinced of the step:

>Because `B` defeats `Exp^{msKS}_{pqARKG-H,B}` given any PRF, `B` must also succeed given this relaxed PRF.
since with a weak PRF, this extension introduces an opportunity for the adversary
to choose `b` and `aux` such that the PRF outputs `tau = -b`,
meaning `O_sk'` would return the unblinded private seed `sk`.
In particular, this is easy if the PRF simply ignores the `b`-based parameter.
Therefore this security argument should in some way be conditioned on the unpredictability of the PRF
in the `b` parameter, but it currently does not
(there is an implicit dependency on the PRF in the reduction to `Adv^{msKS}_{pqARKG}`,
but that advantage is quantified with the pqARKG PRF rather than the pqARKG-H PRF).


## Acknowledgements

Thanks to Sander Dijkhuis (@sander) for proposing the construction with mixing `pk^b_Delta` into the PRF instead of `b`.
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