Bitcoin currently uses the ECDSA algorithm to generate cryptographic signatures for a given message and secp256k1 keypair. Schnorr is an alternative algorithm with several advantages. One key advantage is that when multiple keys are used to sign the same message with Schnorr, the resulting signatures can be combined into a single signature. This can be used to significantly reduce the size of multisig payments and other multisig related transactions, for example lightning channel transactions.| en.bitcoin.it
This post continues a long, wonky discussion of Schnorr signature schemes and the Dilithium post-quantum signature. You may want to start with Part 1. In the previous post I discussed the intuition…| A Few Thoughts on Cryptographic Engineering
This is a graph of secp256k1's elliptic curve y2 = x3 + 7 over the real numbers. Note that because secp256k1 is actually defined over the field Zp, its graph will in reality look like random scattered points, not anything like this.secp256k1 refers to the parameters of the elliptic curve used in Bitcoin's public-key cryptography, and is defined in Standards for Efficient Cryptography (SEC) (Certicom Research, http://www.secg.org/sec2-v2.pdf). Currently Bitcoin uses secp256k1 with the ECDSA al...| en.bitcoin.it