Do the weakness #2 (revealed public key) no need to brute all 116 bits (2^116), and only square root of total length is enough --> 58 bits (2^58). However it is still very much to brute force. Assuming that the monster could be symmetric (116/2 = 58bits unknown bits only), it is enough to make only square root from 2^58 operations --> 2^29. This is possible to find very fast.
Exact. I created Giant Step hashtable for 2^29 symmetrical combinations. Then, check Baby Step for second half of picture, also 2^29 symmetrical combinations.
Border+one half = Giant Step
second half - public key = Baby step
Memory spent for giant step is about 6Gb, can be safe reduced to 3-4Gb. 20 minutes to build hashtable.
baby step takes about 2 minutes to find key.
BSGS can be used for keys up to 70-75 bits.