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# EIP-4399: Supplant DIFFICULTY opcode with PREVRANDAO Source

### Expose beacon chain randomness in the EVM by supplanting DIFFICULTY opcode semantics

Author Mikhail Kalinin, Danny Ryan https://ethereum-magicians.org/t/eip-4399-supplant-difficulty-opcode-with-random/7368 Review Standards Track Core 2021-10-30 3675

## Abstract

This EIP supplants the semantics of the return value of existing DIFFICULTY (0x44) opcode and renames the opcode to PREVRANDAO (0x44).

The return value of the DIFFICULTY (0x44) instruction after this change is the output of the randomness beacon provided by the beacon chain.

## Motivation

Applications may benefit from using the randomness accumulated by the beacon chain. Thus, randomness outputs produced by the beacon chain should be accessible in the EVM.

At the point of TRANSITION_BLOCK of the Proof-of-Stake (PoS) upgrade described in EIP-3675, the difficulty block field MUST be 0 thereafter because there is no longer any Proof-of-Work (PoW) seal on the block. This means that the DIFFICULTY (0x44) instruction no longer has it’s previous semantic meaning, nor a clear “correct” value to return.

Given prior analysis on the usage of DIFFICULTY, the value returned by the instruction mixed with other values is a common pattern used by smart contracts to obtain randomness. The instruction with the same number as the DIFFICULTY opcode returning outputs of the beacon chain RANDAO implementation makes the upgrade to PoS backwards compatible for existing smart contracts obtaining randomness from the DIFFICULTY instruction.

Additionally, changes proposed by this EIP allow for smart contracts to determine whether the upgrade to the PoS has already happened. This can be done by analyzing the return value of the DIFFICULTY instruction. A value greater than 2**64 indicates that the transaction is being executed in the PoS block. Decompilers and other similar tooling may also use this trick to discern the new semantics of the instruction if data of the block including the transaction in question is available.

## Specification

### Definitions

• TRANSITION_BLOCK The definition of this block can be found in the Definitions section of EIP-3675.

### Block structure

Beginning with TRANSITION_BLOCK, client software MUST set the value of the mixHash, i.e. the field with the number 13 (0-indexed) in a block header, to the latest RANDAO mix of the post beacon state of the previous block.

### EVM

Beginning with TRANSITION_BLOCK, the DIFFICULTY (0x44) instruction MUST return the value of the mixHash field.

Note: The gas cost of the DIFFICULTY (0x44) opcode remains unchanged.

### Renaming

The mixHash field SHOULD further be renamed to prevRandao.

The DIFFICULTY (0x44) opcode SHOULD further be renamed to PREVRANDAO (0x44).

## Rationale

### Including RANDAO output in the block header

Including a RANDAO output in the block header provides a straightforward method of accessing it from inside of the EVM as block header data is already available in the EVM context.

Additionally, this ensures that the execution layer can be fully executed with the block alone rather than requiring extra inputs from the PoS consensus layer.

Mixing the randomness into a block header may contribute to uniqueness of the block hash in the case when values of other fields of the block header match the corresponding values of the header of another block.

### Using mixHash field instead of difficulty

The mixHash header field is used instead of difficulty to avoid a class of hidden forkchoice bugs after the PoS upgrade.

Client software implementing pre-EIP-3675 logic heavily depends on the difficulty value as total difficulty computation is the basis of the PoW fork choice rule. Setting the difficulty field to 0 at the PoS upgrade aims to reduce the surface of bugs related to the total difficulty value growing after the upgrade.

Additionally, any latent total difficulty computation after the PoS upgrade would become overflow prone if the randomness output supplanted the value of the difficulty field.

### Reusing existing field instead of appending a new one

The mixHash field is deprecated at the PoS upgrade and set to zero bytes array thereafter. Reusing an existing field as a place for the randomness output saves 32 bytes per block and effectively removes the deprecation of one of the fields induced by the upgrade.

### Reusing the DIFFICULTY opcode instead of introducing a new one

See the Motivation.

### Renaming the field and the opcode

The renaming should be done to make the field and the opcode names semantically sound.

### Using TRANSITION_BLOCK rather than a block or slot number

By utilizing TRANSITION_BLOCK to trigger the change in logic defined in this EIP rather than a block or slot number, this EIP is tightly coupled to the PoS upgrade defined by EIP-3675.

By tightly coupling to the PoS upgrade, we ensure that there is no discontinuity for the usecase of this opcode for randomness – the primary motivation for re-using DIFFICULTY rather than creating a new opcode.

### Using 2**64 threshold to determine PoS blocks

The probability of RANDAO value to fall into the range between 0 and 2**64 and, thus, to be mixed with PoW difficulty values, is drastically low. Though, proposed threshold might seem to have insufficient distance from difficulty values on Ethereum Mainnet (they are currently around 2**54), it requires a thousand times increase of the hashrate to make this threshold insecure. Such an increase is considered impossible to occur before the upcoming consensus upgrade.

## Backwards Compatibility

This EIP introduces backward incompatible changes to the execution and validation of EVM state transitions. As written, this EIP utilizes TRANSITION_BLOCK and is thus tightly coupled with the PoS upgrade introduced in EIP-3675. If this EIP is to be adopted, it MUST be scheduled at the same time as EIP-3675.

Additionally, the changes proposed might be backward incompatible for the following categories of applications:

• Applications that use the value returned by the DIFFICULTY opcode as the PoW difficulty parameter
• Applications with logic that depends on the DIFFICULTY opcode returning a relatively small number with respect to the full 256-bit size of the field.

The first category is already affected by switching the consensus mechanism to PoS and no additional breaking changes are introduced by this specification.

The second category is comprised of applications that use the return value of the DIFFICULTY opcode in operations that might cause either overflow or underflow errors. While it is theoretically possible to author an application where a change in the range of possible values this opcode may return could lead to a security vulnerability, the chances of that are negligible.

## Test Cases

• In one of ancestors of TRANSITION_BLOCK deploy a contract that stores return value of DIFFICULTY (0x44) to the state
• Check that value returned by DIFFICULTY (0x44) in transaction executed within the parent of TRANSITION_BLOCK equals difficulty field value
• Check that value returned by PREVRANDAO (0x44) in transaction executed within TRANSITION_BLOCK equals prevRandao field value

## Security Considerations

The PREVRANDAO (0x44) opcode in PoS Ethereum (based on the beacon chain RANDAO implementation) is a source of randomness with different properties to the randomness supplied by BLOCKHASH (0x40) or DIFFICULTY (0x44) opcodes in the PoW network.

### Biasability

The beacon chain RANDAO implementation gives every block proposer 1 bit of influence power per slot. Proposer may deliberately refuse to propose a block on the opportunity cost of proposer and transaction fees to prevent beacon chain randomness (a RANDAO mix) from being updated in a particular slot.

An effect of proposer’s influence power is limited in time and lasts until the first honest RANDAO reveal is made afterwards. This limitation does also exist in the case when proposers of n consecutive slots are colluding to get n bits of influence power. Simply speaking, one honest block proposal is enough to unbias the RANDAO even if it was biased during several slots in a row.

Additionally, semantics of the PREVRANDAO (0x44) instruction gives proposers another way to gain 1 bit of influence power on applications. Biased proposer may censor a rolling the dice transaction to force it to be included into the next block, thus, force it to use a RANDAO mix that the proposer knows in advance. The opportunity cost in this case would be negligible.

### Predictability

Obviously, historical randomness provided by any decentralized oracle is 100% predictable. On the contrary, the randomness that is revealed in the future is predictable up to a limited extent.

A list of inputs influencing future randomness on the beacon chain consists of but is not limited to the following items:

• Accumulated randomness. A RANDAO mix produced by the beacon chain in the last slot of epoch N is the main input to the function defining block proposers in each slot of epoch N + MIN_SEED_LOOKAHEAD + 1, i.e. it is the main factor defining future RANDAO revealers.
• Number of active validators. A number of active validators throughout an epoch is another input to the block proposer function.
• Effective balance. All else being equal, the lower the effective balance of a validator the lower the chance this validator has to be designated as a proposer in a slot.
• Accidentally missed proposals. Network conditions and other factors that are resulting in accidentally missed proposals is a source of highly qualitative entropy that impacts RANDAO mixes. Usual rate of missed proposals on the Mainnet is about 1%.

These inputs may be predictable and malleable on a short range of slots but the longer the attempted lookahead the more entropy is accumulated by the beacon chain.

### Tips for application developers

The following tips attempt to reduce predictability and biasability of randomness outputs returned by PREVRANDAO (0x44):

1. Make your applications rely on the future randomness with a reasonably high lookahead. For example, an application stops accepting bids at the end of epoch K and uses a RANDAO mix produced in slot K + N + ε to roll the dice, where N is a lookahead in epochs and ε is a few slots into epoch N + 1.
2. At least four epochs of lookahead results in the following outcome:
• A proposer set of epoch N + 1 isn’t known at the end of epoch K breaking a direct link between bidders and dice rollers
• A number of active validators is updated at the end of each epoch affecting a set of proposers of next epochs, thus, impacting a RANDAO mix used by the application to roll the dice
• Due to Mainnet statistics, there is about a 100% chance for the network to accidentally miss a proposal during this period of time which reduces predictability of a RANDAO mix used to roll the dice.
3. Setting ε to a small number, e.g. 2 or 4 slots, gives a third party a little time to gain influence power on the future randomness that is being used to roll the dice. This amount of time is defined by MIN_SEED_LOOKAHEAD parameter and is about 6 minutes on the Mainnet.

A reasonably high distance between bidding and rolling the dice attempts to leave low chance for bidders controlling a subset of validators to directly exploit their influence power. Ultimately, this chance depends on the type of the game and on a number of controlled validators. For instance, a chance of a single validator to affect a one-time game is negligible, and becomes bigger for multiple validators in a repeated game scenario.

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