Multiple Signers and Key Aggregation with Schnorr

Let’s say that Bob and Wendy want to purchase a house from Alice, but where Alice wants a joint digital signature on the transaction. Normally for digital signatures, we would get Bob and Wendy to each digitally sign for the transaction, and add their public kes and their signatures. This becomes inefficient as we scale the number of signers. With the Schnorr signature method, we can simply aggregate signers together, and also aggregate public keys, in order to produce a single signature and public key.

With the Schnorr signature method, we can simply perform an add operation. Let’s first abstract the process, and then I will explain it. In this case, Bob and Wendy want to sign off a transaction (M) they have created:

In most signature methods, we would have to add an ECDSA signature for each of the signers, but with the Schnorr signature method, we can simply add the Schnorr signatures together, and also add the public keys together. With this, Bob will generate his private key (sk_1) and derive his public key from:

He will then generate: