I'm taking a ASP.NET security course on OpenID Connect authorization code workflow with PKCE protection against code replay attack. There is one aspect of this process that I don't understand.
The process:
Relying client generates PKCE code_verifier, hash it into code_challenge, and send the user to the authorization server with the code_challenge as a query parameter.
The authorization server stores the code_challenge, issues authorization code, and redirects user back to client with the authorization code.
The client sends the authorization code along with the original code_verifier to exchange for tokens. The authorization server verifies that the code_verifier indeed hashes into code_challenge before issuing the token.
My question is step #3: since HTTP is stateless, how does the client know which code_verifier to send along with the authorization code? Is this code_verifier stored in a cookie on the user agent?