k, k-parameter: The desired number of stake pools for decentralization, which inversely sets a "soft cap" on the stake pools saturation limit (size). The pool size is determined by total circulating supply divided by k number of pools. Pool size is encouraged to converge toward k for optimal staking rewards, in theory.
k-effective: The “average resulting decentralization” or "effective decentralization" taking into account groups or entities of stake pools. One group could be running multiple stake pools, which lowers the realistic, effective decentralization.
Nakamoto Coefficient, Minimum Attack Vector (MAV): The minimum number of entities in a given subsystem required to get to 51% of the total capacity, or more simply, how many stake pool groups it would take to gain 51% control of the blockchain. This is a simple yet decisive decentralization measurement. It is not limited to pools, but any attack vector. However, for the scope of this paper it is assumed to be pools only. The Nakamoto Coefficient is approximately half of k-effective rounded up to the nearest integer.
Sybil Attack: An attack where the attacker pretends to be an honest pool or pools to gather stake and power in the network. The attacker can create an infinite number of pools in his effort to maximize his own power in the network.
Pledge: The amount of stake pledged by a stake pool in ADA. This combats a sybil attack with an economic cost of a "down-payment" or stake pool pledge when creating a new stake pool.
Pledge Leverage, L: The ratio between an entity’s pool stake and pledge defined by the parameter L. A leverage-based stake pool saturation is based on pledge rather than a fixed size driven by k-parameter. An entity having high leverage means its total stake is much higher than its pledge.
VRF Score: Verifiable Random Function (VRF) score is essentially the lowest random number generated by the stake pools that determines what pool won the slot leader battle to mint a block. The lowest random number VFR score generated by a pool wins the block.
Private vs Public Stake Pools: Cardano stake pool operators can be either private, using only their own self-bonded stake, or public, by accepting delegation. A private stake pool retains 100% of the pool’s profits but must also provide 100% of the pool’s staking power. Most stake pool explorers will not give the pool visibility as a staking option because they are already fully saturated. Private stake pool operators optimize rewards by pledging the whole stake cap for their pool. If you have enough ADA to meet the saturation point alone, your rewards will be 100% of the potential earned when adjusted for the a0 parameter. Public stake pools that do not have full pledge must make up their stake from public delegation.
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Quantifying Decentralization by Balaji Srinivasan
"That is, we define the Nakamoto coefficient as the minimum number of entities in a given subsystem required to get to 51% of the total capacity. Aggregating this measure by taking the minimum of the minimum across subsystems then gives us the “minimum Nakamoto coefficient”, which is the number of entities we need to compromise in order to compromise the system as a whole."
- The Cardano Minimum Attack Vector (And why you should care)
by Leantros Holleman
"Minimum Attack Vector (MAV) The minimum attack vector is the minimum subset of participants that one would need to take under control in order to attack or manipulate the network, by having control of over 51% of the created blocks one could cause havoc to the network"
- "'K-effective' is hereby used to measure the 'average resulting decentralization' and is computed using Equation 1. The Nakamoto Coefficient is approximately half of k-effective rounded up to the nearest integer. K-effective provides a higher resolution quantification of network decentralization compared to the Nakamoto Coefficient." [Ref CIP-50, Liesenfelt, Motivation, 3rd paragraph]
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ELI5 VRF – Understand Verifiable Random Functions, by Crypto Bill of crypto.bi
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The cryptography behind Cardano blocks by Cardanians.io (CRDNS pool)
"The selection of a slot leader is based on randomness. In the ideal case, only one slot leader is selected in a given slot."
"Verifiable Random Function (VRF) key pair. The key is used to find out whether a node is a slot leader in an ongoing slot. The node does it every second."
"As we have said above, it can happen that two nodes become slot leaders in the same slot and both produce valid blocks. Only one of them can be appended to the blockchain. Thus, when validators receive two valid blocks and they need to choose one of them. There is a very simple rule that determines which block will win. Validators append the block that has lower VRF proof. You can imagine it as a comparison of two numbers. The block with the higher VRF proof is orphaned. It means it is thrown away together with all transactions."
- The VRF Score is the lowest random number generated that determines what pool won the block.
- An attack where the attacker pretends to be an honest pool to gather stake or power in the network, the attacker can create an infinite number of pools in his effort to get maximize his own power in the network [Ref]. This is prevented in Cardano by the pledge, or an economic cost to open a stake pool using a "down payment":
"When registering a pool, the pool operator can decide to ‘pledge’ some of his personal stake to the pool. Pledging more will slightly increase the potential rewards of his pool." Preventing Sybil Attacks by Lars Brunjes
- Sybil Attack, Wikipedia
"A Sybil attack is a type of attack on a computer network service in which an attacker subverts the service's reputation system by creating a large number of pseudonymous identities and uses them to gain a disproportionately large influence."
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CIP - Leverage-based Saturation and Pledge Benefit by TobiasFancee
"leverage-based saturation and pledge benefit."
"It has been evident for quite some time that the current incentives and fee structure of the Cardano blockchain are lacking. Cardano’s Nakamoto Coefficient is in steady decline and the emergence of initial stake pool offerings (ISPOs) on the network has only accelerated the path to centralization. The inadequacy of the current protocol stems not from one’s ability to operate multiple pools, but from the lack of a mechanism to limit the leverage of the entities that participate in staking. Leverage is defined as the ratio between an entity’s stake and pledge. An entity having high leverage means its total stake is much higher than its pledge. This is bad in that it reduces the amount of stake that other entities can use for block production."
"Definitions: Pool Stake - Total stake delegated to a stake pool in ADA. Pledge - Amount of stake pledged by a stake pool in ADA. Leverage - The ratio between Pool Stake and Pledge. Pledge Benefit - The reward a stake pool earns for their pledge in ADA in a single epoch. Total Rewards - The total reward a stake pool earns in ADA in a single epoch (includes pledge benefit). APY - Annual Percentage Yield, the expected annual return on investment for staking represented as a percentage of the original investment."
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Stake Pool Operation, Cardano Docs
"A public stake pool is a Cardano network node with a public address that other users can delegate to, and receive rewards. Private stake pools only deliver rewards to their owners."
"Yes, this is technically possible. It can be achieved by registering a stake pool and setting the operator rewards percentage to 100%, so that anybody that delegates to your stake pool will not receive any rewards. This will disincentivize delegators from delegating to you, but provide you with the ability to stake your ada and singly reap the rewards, while testing your stake pool operations."
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Cardano’s stake pool pledge and margin mechanics, Coinbase, Discover, Solutions
"Cardano stake pool operators can be either private, using only their own self-bonded stake, or public, by accepting delegation.
"A private stake pool retains 100% of the pool’s profits but must also provide 100% of the pool’s staking power."
"Alternatively, accepting delegation increases the number of entities that can contribute to a pool’s stake, but also increases the number of entities that receive the rewards as delegators get a pro‐rata share of the pool’s profits. By default, a pool with a margin set below 100% is considered a public pool; ADA holders may choose to delegate their stake to it. A stake pool is by default private if its margin rate is set to 100%—meaning that the stake pool operator retains 100% of the pool’s profit margin. As such, delegators should not delegate to it as they do not earn any rewards for their delegation, and most stake pool explorers will not give the pool visibility as a staking option for that reason. When setting up their stake pool, an operator must decide whether it will be public or private. Once that is determined they can go about optimizing their participation and expected rewards."
"Optimized pledging for private and public pools Private stake pool operators optimize rewards by pledging the whole stake cap for their pool. If you have enough ADA to meet the saturation point alone, your rewards will be 100% of the potential earned when adjusted for the a0 parameter."