Crooked Indifferentiability Revisited
This work addresses security gaps in cryptographic hash functions under subverted primitives, solving an open problem and providing more efficient proofs for the research community.
The paper identifies flaws in a prior proof of crooked indifferentiability for the EXor hash function construction and provides a revised proof that removes restrictions on adversary queries, while also demonstrating that the sponge construction achieves crooked indifferentiability with significantly fewer random bits, offering a quadratic improvement.
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.