While the post-quantum security of "classical" (i.e. bit-oriented) hash functions such as SHA-2 has been a topic of significant discussion, I am finding it challenging to locate detailed information about the post-quantum security of arithmetization-oriented hash functions.
Algebraic hash functions such as Poseidon or Rescue are typically designed generically, allowing them to be instantiated with different prime fields and tailored to various security levels.
Given that these designs differ fundamentally from classical hash functions, I am curious whether it is also recommended to double the security parameters (i.e. field size) to address quantum computing threats, and if so, whether this adjustment alone is sufficient or if additional measures are necessary.
