Cryptanalysing UOV when the vinegar generation process is deterministic and controllable

Factoring RSA modulus with a setup similar to the Approximate Common Divisor problem

Solving an instance of the LWE problem with errors sourced from a known trinomial distribution

Elliptic curve shenanigans, followed by some sagemath magic, some meet in the middle, and truncated LCGs with an instance of the Hidden Number problem