# EIP-2098: Compact Signature Representation Source

### A compact representation of an Ethereum Signature.

Author Richard Moore, Nick Johnson https://github.com/ethereum/EIPs/issues/2440 Final Standards Track ERC 2019-03-14 2

## Abstract

The secp256k1 curve permits the computation of the public key of signed digest when coupled with a signature, which is used implicitly to establish the origin of a transaction from an Externally Owned Account as well as on-chain in EVM contracts for example, in meta-transactions and multi-sig contracts.

Currently signatures require 65 bytes to represent, which when aligned to 256-bit words, requires 96 bytes (with 31 zero bytes injected). The yParity in RLP-encoded transactions also require (on average) 1.5 bytes. With compact signatures, this can be reduced to 64 bytes, which remains 64 bytes when word-aligned, and in the case of RLP-encoded transactions saves the 1.5 bytes required for the yParity.

## Motivation

The motivations for a compact representation are to simplify handling transactions in client code, reduce gas costs and reduce transaction sizes.

## Specification

A secp256k1 signature is made up of 3 parameters, r, s and yParity. The r represents the x component on the curve (from which the y can be computed), and the s represents the challenge solution for signing by a private key. Due to the symmetric nature of an elliptic curve, a yParity is required, which indicates which of the 2 possible solutions was intended, by indicating its parity (odd-ness).

Two key observations are required to create a compact representation.

First, the yParity parameter is always either 0 or 1 (canonically the values used have historically been 27 and 28, as these values didn’t collide with other binary prefixes used in Bitcoin).

Second, the top bit of the s parameters is always 0, due to the use of canonical signatures which flip the solution parity to prevent negative values, which was introduced as a constraint in Homestead.

So, we can hijack the top bit in the s parameter to store the value of yParity, resulting in:

[256-bit r value][1-bit yParity value][255-bit s value]


### Example Implementation In Python

# Assume yParity is 0 or 1, normalized from the canonical 27 or 28
def to_compact(r, s, yParity):
return {
"r": r,
"yParityAndS": (yParity << 255) | s
}

def to_canonical(r, yParityAndS):
return {
"r": r,
"s": yParityAndS & ((1 << 255) - 1),
"yParity": (yParityAndS >> 255)
}


## Rationale

The compact representation proposed is simple to both compose and decompose in clients and in Solidity, so that it can be easily (and intuitively) supported, while reducing transaction sizes and gas costs.

## Backwards Compatibility

The Compact Representation does not collide with canonical signature as it uses 2 parameters (r, yParityAndS) and is 64 bytes long while canonical signatures involve 3 separate parameters (r, s, yParity) and are 65 bytes long.

## Test Cases

Private Key: 0x1234567890123456789012345678901234567890123456789012345678901234
Message: "Hello World"
Signature:
r:  0x68a020a209d3d56c46f38cc50a33f704f4a9a10a59377f8dd762ac66910e9b90
v:  27
Compact Signature:
r:           0x68a020a209d3d56c46f38cc50a33f704f4a9a10a59377f8dd762ac66910e9b90

Private Key: 0x1234567890123456789012345678901234567890123456789012345678901234
Message: "It's a small(er) world"
Signature:
r:  0x9328da16089fcba9bececa81663203989f2df5fe1faa6291a45381c81bd17f76
v:  28
Compact Signature:
r:           0x9328da16089fcba9bececa81663203989f2df5fe1faa6291a45381c81bd17f76


## Reference Implementation

The ethers.js library supports this in v5 as an unofficial property of split signatures (i.e. sig._vs), but should be considered an internal property that may change at discretion of the community and any changes to this EIP.

## Security Considerations

There are no additional security concerns introduced by this EIP.

Copyright and related rights waived via CC0.