I wrote code that solves the subset sum problem via the LLL algorithm, as given in chapter three of the Handbook of Applied Cryptography https://cacr.uwaterloo.ca/hac/ I ran the code on ten random sets, each with positive integers from one to $2^n$, each with a random subset adding up to a target...

In GCM, GMAC, the additional associated data (AAD) (as well as outputs of subsequent blocks) is multiplied by a polynomial H in GF(2^128). This appears to be doing some secure hashing. Is that what's happening, and if so, is this a general hashing method that's used elsewhere?

These are the current community-specific close reasons: Requests for analyzing ciphertext, finding hash preimages, identifying or decoding some code, or even reviewing full cryptographic designs are off-topic, as the results are rarely useful to anyone else and/or would be too long for this site...