BIP340 Elliptic Curve Signatures

This library follows the BitCoin BIP340 proposal for implementing Schnorr signatures for secp256k1. (See: https://bips.xyz/340)

Much of the code is based upon (stolen from) Aaron Dixon's gist, with my thanks.

The api is very simple:

• sha-256 ([message])
  Returns the sha256 hash of the message. Both the message and the hash are byte-arrays.
• num->bytes ([length n])
  Returns the byte-array representation of the BigInteger n. The array will have the specified length.
• bytes->num ([bytes])
  Returns a BigInteger from a byte-array.
• bytes->hex-string ([byte-array])
  Returns a string containing the hexadecimal representation of the byte-array. This is the inverse of hex-string->bytes.
• hex-string->bytes ([hex-string])
  returns a byte-array containing the bytes described by the hex-string. This is the inverse of bytes->hex-string.
• pub-key ([private-key])
  returns the public-key for a given private key. Both are byte-arrays of length 32.
• sign ([private-key message])
  Returns the 64 byte signature of the message and the private key. The message and the private key are byte-arrays.
• verify ([public-key message signature])
  Returns true if the public-key proves that the message was signed using the private key. Otherwise returns nil. The public-key and the message are byte-arrays of length 32. The signature is a byte-array of length 64.

Notes:

• The three tag-hash constants [challenge-tag-hash aux-tag-hash nonce-tag-hash] should probably not be publicly known. We need a way to initialize them in a secure way.
• The algorithms are pretty slow. For high volume relays they would need a lot of optimization.