bpo-45536: Check OpenSSL APIs in configure (GH-29088)

(cherry picked from commit 81520fe677d15cc7f9af5140bc5f9eca8409ad90)

Co-authored-by: Christian Heimes <christian@python.org>
diff --git a/configure.ac b/configure.ac
index c4abac6..4c2ac59 100644
--- a/configure.ac
+++ b/configure.ac
@@ -5831,6 +5831,48 @@
 AC_MSG_RESULT($OPENSSL_RPATH)
 AC_SUBST([OPENSSL_RPATH])
 
+# check if OpenSSL libraries work as expected
+AC_MSG_CHECKING(whether OpenSSL provides required APIs)
+save_LIBS="$LIBS"
+save_CFLAGS="$CFLAGS"
+save_LDFLAGS="$LDFLAGS"
+LIBS="$LIBS $OPENSSL_LIBS"
+CFLAGS="$CFLAGS_NODIST $OPENSSL_INCLUDES"
+LDFLAGS="$LDFLAGS $OPENSSL_LDFLAGS"
+
+AC_LINK_IFELSE([AC_LANG_PROGRAM([[
+#include <openssl/opensslv.h>
+#include <openssl/evp.h>
+#include <openssl/ssl.h>
+
+#if OPENSSL_VERSION_NUMBER < 0x10101000L
+#error "OpenSSL >= 1.1.1 is required"
+#endif
+
+static void keylog_cb(const SSL *ssl, const char *line) {}
+]], [[
+/* SSL APIs */
+SSL_CTX *ctx = SSL_CTX_new(TLS_client_method());
+SSL_CTX_set_keylog_callback(ctx, keylog_cb);
+SSL *ssl = SSL_new(ctx);
+X509_VERIFY_PARAM *param = SSL_get0_param(ssl);
+X509_VERIFY_PARAM_set1_host(param, "python.org", 0);
+SSL_free(ssl);
+SSL_CTX_free(ctx);
+
+/* hashlib APIs */
+OBJ_nid2sn(NID_md5);
+OBJ_nid2sn(NID_sha1);
+OBJ_nid2sn(NID_sha3_512);
+OBJ_nid2sn(NID_blake2b512);
+EVP_PBE_scrypt(NULL, 0, NULL, 0, 2, 8, 1, 0, NULL, 0);
+]])],
+  [AC_MSG_RESULT(yes)],
+  [AC_MSG_RESULT(no)])
+LIBS="$save_LIBS"
+CFLAGS="$save_CFLAGS"
+LDFLAGS="$save_LDFLAGS"
+
 # ssl module default cipher suite string
 AH_TEMPLATE(PY_SSL_DEFAULT_CIPHERS,
   [Default cipher suites list for ssl module.