Contents

• Introduction
• A brief review of digital signatures
• What is a Schnorr signature?
• Why are Schnorr signatures advantageous?
• When will Schnorr signatures be implemented in Bitcoin?
• Summary

Introduction

As we all know, Bitcoin uses the "Elliptic Curve Digital Signature Algorithm" (abbreviated “ECDSA”) to enforce ownership. Through this algorithm, users can derive the public key using a number (that is, the private key).

The magic is that the public key can be easily obtained from the private key, but the reverse operation cannot be achieved. The private key is a passport into the Bitcoin network, able to generate an address to receive tokens and allow users to spend the tokens at a later stage.

In this article, we will take a look at the alternative to ECDSA, the Schnorr signature algorithm, and the exciting changes it is about to bring to Bitcoin.

A brief review of digital signatures

Digital signatures operate similarly to traditional handwritten signatures, but are more secure. Guaranteed. Anyone can forge a handwritten signature with some effort and time. But even after hundreds of thousands of years, it is difficult to break the powerful digital signature.

Digital signatures have many use cases. Common is the communication of a specific message to the public. As mentioned earlier, a public key is created from a private key (a string of numbers that needs to be kept secret), and this process is accomplished using the complex mathematics of the secp256k1 curve. Next, the public address can also be generated through the public key.

Please note that sharing public keys with others is absolutely safe. The public key is published on a personal website or Twitter profile, and others can verify the identity of the publisher. Likewise, a public address can be shared with others in order to receive cryptocurrency sent by others.

Personal digital signatures can be created through private keys. Signed messages are created by composing a message and performing operations with the private key. Anyone compares the signature information with the personal public key to check the authenticity of the signature.

What does this have to do with Bitcoin? In fact, all Bitcoin transactions contain digital signature information, indicating "I am sending the tokens I received previously". When the information is sent to other nodes in the network, the nodes verify that the ECDSA signature matches it. If there is no match, the node will reject the message.

What is Schnorr signature?

Schnorr signature is a completely different mechanism. It operates similarly to the currently used elliptic curve digital signature algorithm, but its advantages are more prominent. In fact, Schnorr signatures predate ECDSA, so many people are curious why this mechanism was not used in Bitcoin in the first place.

A reasonable explanation is that the inventor of the mechanism, Clasu P. Schnorr, applied for a patent. The patent expired in early 2008, before the Bitcoin white paper was released, but the mechanism had not yet been fully standardized at the time. Therefore, Satoshi Nakamoto chose the more widely accepted open source ECDSA.

Why does Schnorr signature have advantages?

Compared with other mechanisms, Schnorr signature is much simpler. Therefore, it is also more secure than other alternative mechanisms. The Schnorr signature may not seem to make much sense at first glance, but it has another powerful property: linearity.

In layman's terms, a mechanism with this feature is more suitable for certain operations, especially multi-signature transactions. As we all know, Bitcoin already supports multi-signature, but the effect is not satisfactory.

When a user creates a multi-signature address, the sender of funds does not need to know the spending conditions set by the user, or even knows that he is sending funds to the multi-signature setting. The only special thing about the address is that it ends with "3" beginning.

However, its true nature is revealed when it comes time to move funds. Suppose someone uses the settings with Alice and Bob at the same time. For one person to spend 5 Bitcoins, three people must provide public keys and valid signatures at the same time. If funds are transferred out of an address, the entire network will know about it by looking at the blockchain.

From a privacy perspective, this model is not ideal. In addition, if you create a more complex multi-signature (for example, 10 people sign and 8 people need to approve), it will take up more space in the blockchain. This results in a lengthy transaction and is therefore expensive. Remember, the more bytes in a transaction, the more fees you pay.

Schnorr signatures are considered a privacy and scalability solution. As we can see, Schnorr signature supports signature aggregation, that is, the signatures of multiple signers are combined into a single signature. In this way, the "main signature" is the same length as a regular single signature, thus greatly saving space.

Furthermore, it is difficult for an onlooker to identify who signed (or did not sign) the transaction from the mix of signatures. In other words, in the  m-m mechanism, funds can only be used after all participants sign, and others cannot tell whether this is a single-party transaction or a multi-signature transaction.

The key is that Schnorr signatures are the cornerstone of the further development of the blockchain. Once implemented, signatures can be used to improve cryptocurrency-related technologies such as atomic swaps and the Lightning Network.

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When will Schnorr signatures be implemented in Bitcoin?

The specific time has not yet been determined. Like most upgrades to the Bitcoin protocol, Schnorr signatures will need to gain acceptance from the wider Bitcoin user community before they can be implemented, which will still take time. Major Bitcoin contributors Pieter Wuille, Jonas Nick, and Tim Ruffing have submitted a Bitcoin Improvement Proposal (BIP), but there are still some areas that need to be improved.

Blockstream has released the MuSig signature scheme. This scheme allows for signature and key aggregation and is likely to become the basis for Bitcoin’s own Schnorr signature mechanism.

Schnorr signatures can be incorporated into the code as a soft fork, meaning the change will not split the network. Instead, this upgrade will require an "opt-in." Despite this, it is optimistically estimated that the integration of Schnorr signatures is just around the corner, but reaching consensus will not happen overnight.

Summary

Schnorr signatures are one of the most high-profile milestones in Bitcoin’s current roadmap. With just one upgrade, privacy and scalability will change dramatically. Moreover, Schnorr signatures can also pave the way for the further development of higher-order structures such as Bitcoin smart contracts and Taproot.