  In CRYPTO 2018, Russell et al introduced the notion of crooked
indifferentiability to analyze the security of a hash function when the
underlying primitive is subverted. They showed that the $n$-bit to $n$-bit
function implemented using enveloped XOR construction (\textsf{EXor}) with
$3n+1$ many $n$-bit functions and $3n^2$-bit random initial vectors (iv) can be
proven secure asymptotically in the crooked indifferentiability setting.
  -We identify several major issues and gaps in the proof by Russel et al, We
show that their proof can achieve security only when the adversary is
restricted to make queries related to a single message.
  - We formalize new technique to prove crooked indifferentiability without
such restrictions. Our technique can handle function dependent subversion. We
apply our technique to provide a revised proof for the \textsf{EXor}
construction.
  - We analyze crooked indifferentiability of the classical sponge
construction. We show, using a simple proof idea, the sponge construction is a
crooked-indifferentiable hash function using only $n$-bit random iv. This is a
quadratic improvement over the {\sf EXor} construction and solves the main open
problem of Russel et al.
