"a measure devised to study consensus security by modeling the profit a miner (or validator, sequencer, or other privileged protocol actor) can make through their ability to arbitrarily include, exclude, or re-order transactions from the blocks they produce"
Don't reveal content of transactions until block inclusion and ordering are committed
Time-lock encryption (Verifiable Delay Functions)
Threshold decryption
Threshold decryption
Messages (transactions) can be encrypted to a single public key
No one knows the private key, but \(n\) parties own "private key shares", such that every subset at least \(t\) parties can decrypt the message, while every subset of at most \(t-1\) parties cannot decrypt.
Distributed key generation and threshold decryption in BFT consensus
Tendermint Proof of Stake: more than 2/3 weight (by stake) of validators vote to commit blocks
Very natural correspondance between "validators" and "private key share owners"
Model
Validators generate a common public key
Alice encrypts her transaction to this public key
Validators include Alice's encrypted transaction in a block
Validators vote with "decryption shares" of Alice's transaction
The block is finalized and Alice's transaction is decrypted and executed
Aligning decryption with consensus
Validators: 2/3 by count \(\ne\) 2/3 by stake
Ideal outcome: validator subset can finalize a block if and only if they can decrypt transactions
Weighting private key shares
Higher stake validators get more private key shares
\(n\) number of private shares -> bandwidth and computation must be \(O(n \log n)\)
Distributed key generation (DKG)
Publicly Verifiable Secret Sharing (PVSS) with no dispute round
In PVSS, the validity of every step of the DKG can be checked by every other validator
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