tl;dr:

1. Notice the seed has 32 bits
2. Calculate inverse matrix in ring modulo `2**64` for independent matrix rows
3. Brute-force all possible seeds
4. Profit!

Fulll writeup: https://github.com/p4-team/ctf/tree/master/2017-12-29-34c3/crypto_lol

Original writeup (https://github.com/p4-team/ctf/tree/master/2017-12-29-34c3/crypto_lol).