CURLcode curl_easy_setopt(CURL *handle, CURLOPT_PROXY_SSL_VERIFYPEER, long verify);
This option tells curl to verifies the authenticity of the HTTPS proxy's certificate. A value of 1 means curl verifies; 0 (zero) means it doesn't.
This is the proxy version of CURLOPT_SSL_VERIFYPEER(3) that's used for ordinary HTTPS servers.
When negotiating a TLS or SSL connection, the server sends a certificate indicating its identity. Curl verifies whether the certificate is authentic, i.e. that you can trust that the server is who the certificate says it is. This trust is based on a chain of digital signatures, rooted in certification authority (CA) certificates you supply. curl uses a default bundle of CA certificates (the path for that is determined at build time) and you can specify alternate certificates with the CURLOPT_PROXY_CAINFO(3) option or the CURLOPT_PROXY_CAPATH(3) option.
When CURLOPT_PROXY_SSL_VERIFYPEER(3) is enabled, and the verification fails to prove that the certificate is authentic, the connection fails. When the option is zero, the peer certificate verification succeeds regardless.
Authenticating the certificate is not enough to be sure about the server. You typically also want to ensure that the server is the server you mean to be talking to. Use CURLOPT_PROXY_SSL_VERIFYHOST(3) for that. The check that the host name in the certificate is valid for the host name you're connecting to is done independently of the CURLOPT_PROXY_SSL_VERIFYPEER(3) option.
WARNING: disabling verification of the certificate allows bad guys to man-in-the-middle the communication without you knowing it. Disabling verification makes the communication insecure. Just having encryption on a transfer is not enough as you cannot be sure that you are communicating with the correct end-point.
CURL *curl = curl_easy_init();
if(curl) {
curl_easy_setopt(curl, CURLOPT_URL, "https://example.com");
/* Set the default value: strict certificate check please */
curl_easy_setopt(curl, CURLOPT_PROXY_SSL_VERIFYPEER, 1L);
curl_easy_perform(curl);
}