Each with slightly different properties I will talk about SPECTRE Designed for payments (not so good for smart contracts).
Insight 1: DAGs are more powerful Direct Revelation. Let each block reveal its full “worldview”
We can still tell what the longest chain is
Insight 2: Bitcoin is related to voting
Consider each block as voting for any chain that contains it (against chains that don’t)
A
B
C
D
E
F
G
H
I
The longest chain wins 9
Cloning in elections Trump Republican Cruz Democrat Clinton
A voting rule is “clone proof” if it then maintains the result of the elections even when one of the alternatives is “cloned” (maintaining order)
10
Plurality is not clone-proof x3
x4
Dem.
Rep.
Rep.
Dem.
x2
x2
Clinton
Trump
Cruz
Trump
Cruz
Trump
Cruz
Clinton
Clinton
x3
A Condorcet loser is elected 11
Cloning in Bitcoin
Trump
Cruz
Clinton
We should “prefer” visible (published) blocks over ones that were hidden. That helps us be clone proof 12
Insight 3: amplification
Miners strengthen the majority decision and thus make it more robust B
A
D
C
E
F
G
H
Add new block here!
I
13
SPECTRE: A Fast and Scalable Cryptocurrency Protocol [Lewenberg, Sompolinsky, Z] https://eprint.iacr.org/2016/1159.pdf
What do miners do? Create blocks with transactions (with PoW) Blocks point to all known “tips” of the DAG That’s it.
Blocks created in parallel may contain conflicting transactions.
Nodes observe (local copy) of DAG decide if Tx is Accepted or Rejected
Accepted TXs
Just like Bitcoin: Accepted
Rejected
But REALLY what we should think of transactions in 3 states: RobustReject, Pending, RobustAccept Just like in Bitcoin: RobustAccept
RobustReject
Pending
Properties that we are aiming for Consistency: Tx is Accepted iff all inputs are accepted and all conflicts are rejected. Safety: If Tx is RobustAccepted by any node, then (with high prob) all nodes will RobustAccept, forever. Weak Liveness: if a Tx is published in DAG and no conflicting Txs are published for a while, it is RobustAccepted quickly. As long as the attacker is
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