If I'm understanding the application correctly, this would also work with Tillich-Zemor-style hashing based on matrix groups. The idea is to map the 0 and 1 message bits onto a pair of generators of a subgroup of the invertible 2x2 matrices with entries in some GF(2^n). The message hash is just the product of the generators corresponding to the message bits.
What's really cool is that matrix multiplication is associative, i.e. x(yz) = (xy)z, so you can perform the hashing in parallel: Hash the left half, hash the right half, and combine the results by multiplication. It also allows distributed multi-party hashing, as in this article's application.
Unfortunately, classical TZ hashing has fallen completely to practical collision attacks as well as first and second preimage attacks. However, those attacks all rely on very special properties of power-of-two Galois fields, so there's no reason generalized TZ-style matrix group hashing wouldn't be feasible.
What's really cool is that matrix multiplication is associative, i.e. x(yz) = (xy)z, so you can perform the hashing in parallel: Hash the left half, hash the right half, and combine the results by multiplication. It also allows distributed multi-party hashing, as in this article's application.
Unfortunately, classical TZ hashing has fallen completely to practical collision attacks as well as first and second preimage attacks. However, those attacks all rely on very special properties of power-of-two Galois fields, so there's no reason generalized TZ-style matrix group hashing wouldn't be feasible.