In the TLS handshake process, the Certificate Verify message will follow the Client Key Exchange message after the server requested a client certificate. The Certificate Verify contains a digital signature computed over all previous handshake messages including the type and length fields of the handshake messages. This process allows the client to prove that it owns the private key of the client certificate it sends to the server.
The idea came from a practical problem. There is an mTLS enabled server that conducts different action policies based on the client certificate received, for example, different welcome pages for different client certificates. If a layer-7 reverse proxy service like the load balancer is placed in front of the proxied server which also requires decrypting the TLS traffic. The proxied server can only get the client certificate information from the HTTP header (for example, set proxy_set_header with $ssl_client_cert variable in NGINX) which requires modifying the logic of the server.
A simple but very troublesome solution is the reverse proxy service stores all the client certificates and their private keys. The reverse proxy service will use the same client certificate it received during the mTLS handshake process to establish the mTLS connection with the proxied server.
Since the reverse proxy service can choose whether to trust the client or not with its own implementation, it is possible to forge the Certificate Verify message by asking the client to send a second Certificate Verify signature when the proxied server needs the reverse proxy service to do so (I know it's like a man-in-the-middle attack)?
