cosine similarity LSH and random hyperplane

I read few solutions about nearest neighbor search in high-dimensions using random hyperplane, but I am still confused about how the buckets work. I have 100 millions of document in the form of 100-dimension vectors and 1 million queries. For each query, I need to find the nearest neighbor based on cosine similarity. The brute force approach is to find cosine value of query with all 100 million documents and select the the ones with value close to 1. I am struggling with the concept of random hyperplanes where I can put the documents in buckets so that I don't have to calculate cosine value 100 million times for each query.