Zero-Knowledge (ZK) has seem a lot utilization and innovation in the past few years, and is thus worth criticial examination. ZK cryptography uses a variety of cryptographic primitives to achieve its goals. These primitives are often based on new and novel mathematics. As a result, the security of these primitives is not as well understood as the security of more traditional primitives like RSA and AES. For example, we rely on the security of algebraic hash functions.

Operating on the premise that ZK will bring massive changes to the world, not just for blockchains but also for the broader technical infrastructure of the world. For example, with applications like privacy preserving machine learning, and MPC, there are boundless benifits of contributing to the security of these cryptographic primitives. However, unless these chemes are proven to be secure, they will not be useful let alone adopted.

It is our target objective to create some evidence for or against the security of algebraic hash functions. We aim are to put together a practical guide to understanding the security assumptions in algebraic hash functions and their known algebraic attacks. We will aim to cover and more deeply understand what the security assumption in Poseidon.