E1ca9558a8c8e23517198fc86277b66d jpeg on May 15, 2019, BCH complete network upgrades in block level 582679. The network upgrade is a performance upgrade that adds two new protocol features to BCH: Segwit recovery and the much anticipated Schnorr signature.

Why were Schnorr signatures introduced?

Both BCH and Bitcoin have been using the elliptic curve digital signature algorithm (ECDSA), which defines a mathematical set for calculation, specifying the key format and a set of values for cryptographic operations. The advantage of ECDSA is that the same security as RSA can be achieved with a smaller key size due to the efficiency of elliptic curve encryption. This makes ECDSA a smart choice for Bitcoin because smaller keys take up less space overall, resulting in less data and faster operation. However, ECDSA- random number reuse can lead to private key disclosure, and ECDSA has scalability issues.

The Schnorr signature can be applied to any mathematical group that satisfies the discrete logarithm problem and has a security proof. And there are no malleability issues with Schnorr signatures; Support batch validation of signatures for different messages; Linear signature Features Schnorr signature native supports aggregation signatures.

Schnorr signature has more advantages than ECDSA signature:

1. Smaller data. Most ECDSA signatures are 71 or 72 bytes. All Schnorr signatures are 64 bytes.

2, high verification efficiency. Compared with ECDSA signature, Schnorr signature takes less time to verify transactions, and more transactions are verified in the same time.

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3. Aggregate signatures. Using Schnorr signature, you can compress a signature with multiple SIG inputs into one signature and combine multiple signatures into one signature. The Schnorr scheme can reduce blockchain storage and bandwidth by at least 25% when a large number of signatures produce an aggregated signature.

4. Enhance privacy. Originally, some users would deliberately use multiple signatures to send transactions to improve privacy, often referred to as MultiSig. A Schnorr signature makes your signature look like any other signature, increasing the privacy of the transaction.

5. Open the door to more complex smart contract architectures. Because now whether the multi-signed transaction type is 2/3, 3/15, or 100/100, all types require the same amount of signature data as single-signed transactions.

6. Schnorr signature can hide the payment channel as atomic swap of ordinary payment. If desired, a network of payment channels in the form of lightning networks and a secure chain (Layer 2) involving unconfirmed transactions involving multiple parties can also be implemented.

7. In addition to scalability and privacy, Schnorr offers a feature for wallet platforms using the protocol: replay protection.

BCH first Schnorr Multisig transaction

After the Bitcoin Cash upgrade was completed, BCH developers rushed to test Schnorr Multisig transactions.

On the night of May 18, 2019, indie developer Mark B. Lundeberg, Chris Pacia, developer of BCH full Node BCHD, and an independent miner named CheckSum0 worked together to create the first transaction on the BCH network using Schnorr Multisig. The deal is a donation to Ross Ulbricht, the founder of the free-trading Silk Road.

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The OP_RETURN message carried in the transaction, decoded, reads: “BCH is about giving people the freedom to make their own choices and pursue their own happiness, whether they personally see fit or not.” In fact, multiSIG is exactly what it implies: transferring funds requires multiple signatures (private keys). This is a particularly important method for cryptocurrency transactions, with another layer of security.

To take a simple example, a husband and wife savings account with multisig signatures cannot transfer funds from their account unless they both agree. This feature not only meets the need for privacy for some users, but also meets the need for multiple users to control a single transaction.

After completing the transaction, the trio released their private keys as evidence:

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They also announced the event on Twitter. @Checksum0 said, “@MarkLundeberg @Chrispacia and I have created the first Schnorr multiple signature in history. The deal is a donation to @free_Ross. Evidence will be released soon. “

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Lundeberg and CheckSum0 then posted their transcripts of historical transactions on GitHub Gist, respectively.

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While the deal is the first of its kind for Schnorr Multisig, Lundeberg cautioned that it is an experiment, a demonstration and not necessarily safe. “Be careful, funds can easily be lost!” .

The choice of Ross Ulbricht’s donation is not only historic, but symbolic. Because the cash nature of protecting relative anonymity and peer-to-peer transactions is often reminiscent of Ross Ulbricht’s dilemma. He was accused of being the mastermind behind Silk Road, which was early evidence that Bitcoin could be used as digital cash in the real world.

The introduction of Schnorr signatures has profound implications for BCH. It not only improves the efficiency of the BCH, but also improves the privacy of the BCH. An outside observer has no way of knowing what the transaction is. It could be a regular transaction, it could be a multi-signed transaction involving 100 people, or it could be another use case that hasn’t been developed yet. Schnorr also allows for things that are impossible in Bitcoin, such as the aforementioned 100-person multiple signature — all of which results in a very small transaction (smaller than a normal P2PKH transaction, whatever OP_RETURN is).

This transaction is only the first manifestation of Schnorr signatures on the BCH network, demonstrating the feasibility of Schnorr signatures on the BCH network. Let’s see what breakthroughs the BCH network will have in the future with the help of Schnorr’s signature!

This article is reprinted from wechat official account BitcoinCash