- We consider leader election in PoS observed over some period of time by an adversary who wants to learn its stake with high “accuracy” and high “confidence”.
- For the probability of stake greater than some threshold derived rigorouslower and upper bounds on this probability.
- For the same probability considered an asymptotic long-time regime and developed a mathematical framework for this regime.
- Verification of above results by simulations is in progress.
- The above will be a part of the framework whichwill be used to get a more accurate estimate ofthe number of layers which are requiredto reduce anonymity failures in the mixnet. More details provided[here](https://www.overleaf.com/read/xvgmfchdhgzh#acd15d)
- Analyzed how stake splitting affected leader rates in Crypsinous: Stake Splitting in Praos
## `data availability`
### `research`
- Designed a new super-commitment structure and explained it [here](https://www.notion.so/1-5d-SuperCommit-4a81bdaf19e64d53a4a158f38c6b6077). After some discussions, we agreed that prover cannot temper the column entries by adding and subtracting some values but he can reorder the column entries. The proof does not guarantee column ordering. Solution methods for this were discussed, but since the focus was on a different structure design, this development was postponed for now.
- Thought of a different design and explained it [here](https://www.notion.so/New-Idea-cddf055558f84137ba19f01ea8fe15c7). The main idea of the design is to take a commitment of commitments. As a result of the investigations, the structure is thought to be working. Cryptographic proof will be worked on.
- The newly designed structures were compared with these existing schemes. It is thought that our current design will provide the whole advantages of [Avail](https://blog.availproject.org/a-guide-to-selecting-the-right-data-availability-layer/ ).
### `development`
- Continuing DA mock implementation - splitting it into reviewable parts
