Discrete Log Implementation of Schnorr Signatures in PowerShell

In Feb 1989, Claus Schnorr submitted a patent which was assigned to no one. It has 11 claims and allowed digital signatures to be merged for multiple signers [here]:

This method has the great advantage that we can have multiple signers to a message or a transaction and end up with a single signature for all the signers. It is now being used in Bitcoin transactions so that we have an efficient signature for a transaction that involves multiple entities.

With the Schnorr signature, we create a signature (r,e) for a hash of the message (m). Initially, Peggy (the prover) has a private key x, and her public key will then be:

and where G is the base point on the curve. She then generates random nonce (k) for the signing of a message and defines a commitment to this value:

Next, with a message (M), she computes a challenge (e) with a hash function of:

Next, Peggy computes:

Peggy then sends e and s to Victor (the verifier). Victor then determines:

If e_v is equal to the e value that Peggy sent, the signature has been proven…