Fountain Codes: a way to reduce blockchain storage costs

The discussion centers around the technical aspects of achieving anonymity in network systems through group connectivity and denial of service (DoS) attacks. When considering a scenario where there are N anonymity groups, and one needs to connect only to a fraction, specifically rN where r is less than 1, the strategy shifts from targeting a single group to needing to compromise the nodes in (1-r)N+1 groups. This approach also necessitates DoS attacks on any remaining full archival nodes, assuming they exist, thereby amplifying the complexity and scale of the attack required.

In the realm of data storage and recovery, each block of data is encoded into multiple parts — for instance, 246 parts — with the requirement that any 10 parts are sufficient to reconstruct the entire block. This encoding method implies that to prevent the reconstruction of a block, access to at least 96% of the nodes, in addition to all archival nodes, must be blocked. Such a system significantly reduces the storage burden on individual nodes by distributing it across many, thus each node only requires a tenth of the total storage capacity.

Furthermore, the discovery process within this system appears robust, as random selection has a high probability — approximately 86% — of achieving all distinct selections without prior knowledge of peer locations within the network. The critique extends to a 2019 study on peeling codes, which highlights some problematic recovery properties such as a high overhead, exceeding 30%, in terms of symbol counts. Additionally, the lack of locality in the described scheme raises concerns about how effectively storage can be managed during the recovery process on a pruning node. This prompts a reconsideration of the advantages this method holds over alternative approaches like striping at the block level, suggesting that further analysis and concrete numerical data are necessary to evaluate efficacy fully.