Whisper theoretical model. Attempts to encode characteristics of it. Goals: 1. Ensure network scales by being user or usage bound, as opposed to bandwidth growing in proportion to network size. 2. Staying with in a reasonable bandwidth limit for limited data plans. 3. Do the above without materially impacting existing nodes. Case 1. Only receiving messages meant for you [naive case] Assumptions: - A1. Envelope size (static): 1024kb - A2. Envelopes / message (static): 10 - A3. Received messages / day (static): 100 - A4. Only receiving messages meant for you. For 100 users, receiving bandwidth is 1000.0KB/day For 10k users, receiving bandwidth is 1000.0KB/day For 1m users, receiving bandwidth is 1000.0KB/day ------------------------------------------------------------ Case 2. Receiving messages for everyone [naive case] Assumptions: - A1. Envelope size (static): 1024kb - A2. Envelopes / message (static): 10 - A3. Received messages / day (static): 100 - A5. Received messages for everyone. For 100 users, receiving bandwidth is 97.7MB/day For 10k users, receiving bandwidth is 9.5GB/day For 1m users, receiving bandwidth is 953.7GB/day ------------------------------------------------------------ Case 3. All private messages go over one discovery topic Assumptions: - A1. Envelope size (static): 1024kb - A2. Envelopes / message (static): 10 - A3. Received messages / day (static): 100 - A6. Proportion of private messages (static): 0.5 - A7. Public messages only received by relevant recipients (static). - A8. All private messages are received by everyone (same topic) (static). For 100 users, receiving bandwidth is 49.3MB/day For 10k users, receiving bandwidth is 4.8GB/day For 1m users, receiving bandwidth is 476.8GB/day ------------------------------------------------------------ Case 4. All private messages are partitioned into shards [naive case] Assumptions: - A1. Envelope size (static): 1024kb - A2. Envelopes / message (static): 10 - A3. Received messages / day (static): 100 - A6. Proportion of private messages (static): 0.5 - A7. Public messages only received by relevant recipients (static). - A9. Private messages are partitioned evenly across partition shards (static), n=5000 For 100 users, receiving bandwidth is 1000.0KB/day For 10k users, receiving bandwidth is 1.5MB/day For 1m users, receiving bandwidth is 98.1MB/day ------------------------------------------------------------ Case 5. Case 4 + All messages are passed through bloom filter with false positive rate Assumptions: - A1. Envelope size (static): 1024kb - A2. Envelopes / message (static): 10 - A3. Received messages / day (static): 100 - A6. Proportion of private messages (static): 0.5 - A7. Public messages only received by relevant recipients (static). - A9. Private messages are partitioned evenly across partition shards (static), n=5000 - A10. Bloom filter size (m) (static): 512 - A11. Bloom filter hash functions (k) (static): 3 - A12. Bloom filter elements, i.e. topics, (n) (static): 100 - A13. Bloom filter assuming optimal k choice (sensitive to m, n). - A14. Bloom filter false positive proportion of full traffic, p=0.1 For 100 users, receiving bandwidth is 10.7MB/day For 10k users, receiving bandwidth is 978.0MB/day For 1m users, receiving bandwidth is 95.5GB/day NOTE: Traffic extremely sensitive to bloom false positives This completely dominates network traffic at scale. With p=1% we get 10k users ~100MB/day and 1m users ~10gb/day) ------------------------------------------------------------ Case 6. Case 5 + Benign duplicate receives Assumptions: - A1. Envelope size (static): 1024kb - A2. Envelopes / message (static): 10 - A3. Received messages / day (static): 100 - A6. Proportion of private messages (static): 0.5 - A7. Public messages only received by relevant recipients (static). - A9. Private messages are partitioned evenly across partition shards (static), n=5000 - A10. Bloom filter size (m) (static): 512 - A11. Bloom filter hash functions (k) (static): 3 - A12. Bloom filter elements, i.e. topics, (n) (static): 100 - A13. Bloom filter assuming optimal k choice (sensitive to m, n). - A14. Bloom filter false positive proportion of full traffic, p=0.1 - A15. Benign duplicate receives factor (static): 2 - A16. No bad envelopes, bad PoW, expired, etc (static). For 100 users, receiving bandwidth is 21.5MB/day For 10k users, receiving bandwidth is 1.9GB/day For 1m users, receiving bandwidth is 190.9GB/day ------------------------------------------------------------ Case 7. Case 6 + Mailserver case under good conditions with smaller bloom false positive and mostly offline Assumptions: - A1. Envelope size (static): 1024kb - A2. Envelopes / message (static): 10 - A3. Received messages / day (static): 100 - A6. Proportion of private messages (static): 0.5 - A7. Public messages only received by relevant recipients (static). - A9. Private messages are partitioned evenly across partition shards (static), n=5000 - A10. Bloom filter size (m) (static): 512 - A11. Bloom filter hash functions (k) (static): 3 - A12. Bloom filter elements, i.e. topics, (n) (static): 100 - A13. Bloom filter assuming optimal k choice (sensitive to m, n). - A14. Bloom filter false positive proportion of full traffic, p=0.1 - A15. Benign duplicate receives factor (static): 2 - A16. No bad envelopes, bad PoW, expired, etc (static). - A17. User is offline p% of the time (static) p=0.9 - A18. No bad request, duplicate messages for mailservers, and overlap/retires are perfect (static). - A19. Mailserver requests can change false positive rate to be p=0.01 For 100 users, receiving bandwidth is 3.9MB/day For 10k users, receiving bandwidth is 284.8MB/day For 1m users, receiving bandwidth is 27.8GB/day ------------------------------------------------------------ Case 8. Waka mode - no metadata protection with bloom filter and one node connected; still static shard Next step up is to either only use contact code, or shard more aggressively. Note that this requires change of other nodes behavior, not just local node. Assumptions: - A1. Envelope size (static): 1024kb - A2. Envelopes / message (static): 10 - A3. Received messages / day (static): 100 - A6. Proportion of private messages (static): 0.5 - A7. Public messages only received by relevant recipients (static). - A9. Private messages are partitioned evenly across partition shards (static), n=5000 For 100 users, receiving bandwidth is 1000.0KB/day For 10k users, receiving bandwidth is 1.5MB/day For 1m users, receiving bandwidth is 98.1MB/day ------------------------------------------------------------