diff --git a/pqarkg-h.md b/pqarkg-h.md index 5528350..b39a536 100644 --- a/pqarkg-h.md +++ b/pqarkg-h.md @@ -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`.