# Signing and Verifying Ethereum Signatures

### If you work with Ethereum, it can help to have a good understanding of how signatures are signed and verified. Let's investigate.

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Join For FreeFor an on-chain Ethereum transaction to be processed, it needs to be included in a block and mined. As a result, on-chain transactions take some time and require gas payment (in Ether) to compensate miners for their work.

Off-chain computation lets you perform actions instantly without waiting for transactions to be mined, and avoids paying any gas costs.

In decentralized exchanges, signatures and off-chain computation are used to pre-authorize market takers to fill any signed orders made by market makers. Instead of posting buy or sell orders directly on-chain, Market Makers sign messages containing their orders with their private key. Market Makers then submits these signed orders to an off-chain order book (hosted on a centralized server) for traders to browse and fill. These off-chain orders are submitted instantly, without having to pay any gas.

The magic ingredient that makes off-chain order books work are cryptographic signatures.

Cryptographic signatures are a foundational computer science primitive that enables all blockchain technology. Signatures can be used to authorize transactions on behalf of the signer. It can also be used to prove to a smart contract that a certain account approved a certain message.

In this article, we’ll look at how you can use Ethereum signatures to validate the origin and integrity of messages. Then, we’ll examine several use cases that utilize signed messages and off-chain computation, such as decentralized exchanges, state channels, and meta transactions.

## Public Key Cryptography

Before we proceed to signature signing and verification works, let’s start by looking at public-key cryptography and the ECDSA algorithm used by the Ethereum blockchain.

### Public Keys and Private Keys

Modern cryptography is founded on the idea that the key that you use to encrypt your data can be made public while the key that is used to to decrypt your data can be kept private. As such, these systems are known as public-key cryptographic systems.

The earliest and most well known of these systems is RSA, which we’ll examine in the next section.

### Trapdoor Functions

A key component of public-key cryptosystems is **Trapdoor Functions**: a set of algorithms that is easy to process in one direction, but hard to undo.

In RSA, the easy algorithm multiplies two large prime numbers. The hard algorithm is factoring the product of two large prime numbers.

However, RSA suffers from increasingly efficient factoring algorithms that have been moderately successful in solving the factorization problem.

Finding a good Trapdoor Function is critical in making a secure public key cryptographic system. The bigger the spread between the difficulty between the easy and hard algorithms/directions, the more secure a cryptographic system based on it will be.

### ECDSA

To address the drawbacks of RSA, alternative cryptographic algorithms were proposed around the mathematics of elliptic curves known as Elliptic Curve Digital Signature Algorithm (ECDSA). An elliptic curve cryptosystem can be defined by picking a prime number as a maximum, a curve equation, and a public point `A`

on the curve:

Take any two points on the curve above and draw a line through them, it will intersect the curve at exactly one more place. Like a game of billiards, you take a ball at point A, shoot it towards point B. When it hits the curve, the ball ‘bounces’ either straight up (when it’s below the x-axis) or straight down (when it’s above the x-axis) to the other side of the curve. Repeat this process `n`

times (this process represents a dot product.)

It turns out that if you have two points, an initial point ‘bounced’ with itself `n`

times to arrive at a final point, finding out `n`

when you only know the final point and the first point is hard. At the same time, it’s easy to repeat over and over following the rules described above.

In an elliptic curve cryptosystem, a private key is a number

`n`

, and a public key is the public point ‘bounced’ with itself`n`

times.

Compared to prime factorization, ECDSA’s elliptic curve logarithm problem is harder to compute. Since a more computationally intensive hard problem means a stronger cryptographic system, it follows that elliptic curve cryptosystems are harder to break than RSA and Diffie-Hellman.

Ethereum signatures uses ECDSA and secp256k1 constants to define the elliptic curve.

## Signing and Verifying Signatures

Each account in the Ethereum network has a public key and a private key. An Ethereum address is essentially a hashed version of the public key.

Accounts can use their private key to sign a piece of data, returning a signature of that data.

Anyone can verify the generated signature to:

- Recover the public key/address of the signer, and
- Verify the integrity of the message, that it is the same message that was signed by the signer.

### Signing

You can sign messages entirely off-chain in the browser, without interacting with the Ethereum network. Signing and the verification of ECDSA-signed messages allows tamper proof communications outside of the blockchain.

We can call the `eth_sign`

method via an Ethereum client such as `web3.js`

:

The

`eth_sign`

method calculates an Ethereum specific signature with:`eth_sign(keccak256("\x19Ethereum Signed Message:\n" + len(message) + message)))`

.The prefix to the message makes the calculated signature recognisable as an Ethereum specific signature.

Note that we can sign messages entirely client-side.

### Mitigating Replay Attacks

Signed messages should contain a nonce of some kind to mitigate against replay attacks. For example, we don’t want someone to be able to submit our buy/sell orders again to execute another transaction. This can be implemented by keeping track of nonces seen so far:

### Signing a Message with Arguments

A message can contain specific details about the action being authorized and any parameters required to execute the action. We can encode these arguments in the message itself.

We can use ethereumjs.ABI.soliditySHA3 to calculate the `sha3`

of given input parameters in the same way Solidity would:

In the above example, we sign a message contains details of our order, containing an `address`

of the owner, `amount`

of tokens, and `nonce`

.

## Verification

ECDSA signatures in Ethereum consist of three parameters `r`

, `s`

, and `v`

. Solidity provides a globally available method `ecrecover`

that returns an address given these three parameters. If the returned address is the same as the signer’s address, then the signature is valid.

Signatures produced by `web3.js`

are the concatenation of `r`

, `s`

, and `v`

, so a necessary first step is splitting those parameters back out.

Smart contracts and Ethereum clients have the ability to verify ECDSA signatures:

The code above defines a `recover(bytes32 hash, bytes signature) returns address`

function that:

- Splits the
`signature`

to its three components`r`

,`s`

, and`v`

, and - Calls
`ecrecover(hash, v, r, s)`

, and - Returns the Ethereum address of the signer that signed the message.

Note that any attempt to tamper the message hash or signature will result in a decoded address that is different than the signer’s address. This ensures that the integrity of the message and signer can be enforced.

At this point, we’ve recovered the signer of the message, but we haven’t validated the integrity message hash. It’s possible that the message is NOT the one that was signed by the owner. To do so, the smart contract needs to know exactly what parameters were signed, and so it must recreate the message from the parameters and use that for signature verification:

In the `submitOrder()`

function above, we construct our `messageHash`

by passing in the original `amount`

and `nonce`

of the original message. These parameters should be published on an off-chain relay server as well for market takers to submit alongside the signature:

Once we’ve verified that the message signer and the message arguments matches, we can process the order:

That’s it! We’ve just made use of signatures to perform an off-chain computation!

## Signatures Use Cases

Let’s look at how cryptographic signatures and off-chain computation are used in the wild. Most of these use cases revolve around minimizing the time spend on-chain and extracting most of the heavy lifting off-chain.

### Decentralized Exchanges

Decentralized exchanges such as EtherDelta and 0x utilizes off-chain computation in order to save gas costs.

In decentralized exchanges, signatures and off-chain computation are used to pre-authorize market takers to fill any signed orders made by market makers. Instead of posting buy or sell orders directly on-chain, Market Makers sign messages containing their orders. Market Makers submits these signed orders to an off-chain order book (hosted on a centralized server.)

Each off-chain order is a signed message indicating that you would like to do a particular trade. Market Takers can browse the order book and select the order they wish to fill by submitting the signed order to a smart contract to be processed and having the funds necessary to do so.

Off-chain computation lets traders post orders instantly without waiting for transactions to be mined, and avoids paying any gas costs!

You can learn more about decentralized exchanges by reading the 0x whitepaper.

### State Channels

State channels are proposed as a means of scaling the Ethereum blockchain and reducing costs for a variety of applications by moving on-chain stateful components for blockchain applications off-chain. This means that the delays and fees associated with transactions can be avoided.

State channels (and Force-Move Games) allow participants to make repeated actions without using transactions.

Participants in a state channel pass cryptographically signed messages back and forth, accumulating intermediate state changes without publishing them to the canonical chain until the channel is closed. State channels are ideal for “bar tab” applications where numerous intermediate state changes may be accumulated off-chain before being settled by a single on-chain transaction (i.e. day trading, poker, turn-based games.)

### Meta Transactions

Today, the barriers of entry for using dApps for regular users who aren’t crypto-savvy is steep. DApps need a significant improvement in UX to hide the complexity of fees and transactions so that it’s more intuitive for users to participate. Meta transaction is an initiative to lower barriers to entry and drive mass Ethereum adoption.

Meta Transactions lets DApps pay gas for first time users. By using cryptographic signatures, etherless accounts can sign meta transactions and incentivize relayers to pay the gas for them (perhaps in exchange for fiat payment.)

Any relayer can submit and execute the meta transaction, paying gas on behalf of the user in exchange from other forms of compensation specified in the meta transaction message. Ether or tokens can be used to pay relayers. For example, this could be the meta transaction:

Instead of sending transactions directly to a smart contract, users sends it to a secondary relayer network. The network can parse meta transactions and ensure the signature is valid. Relayers then pick which transactions are most profitable and interfaces directly with the blockchain.

With meta transactions, users are able to interact with the blockchain from accounts that don’t hold any Ether.

## Summary

Cryptographic signatures are a foundational computer science primitive that enables all blockchain technology. Signatures can be used to authorize transactions on behalf of the signer. It can also be used to prove to a smart contract that a certain account approved a certain message.

In this article, we’ve taken a look at how you can use Ethereum signatures to validate the origin and integrity of messages and perform an off-chain computation. We’ve also looked at how signatures are used for decentralized exchanges, state channels, and meta transactions.

Published at DZone with permission of Yos Riady, DZone MVB. See the original article here.

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