Я окончательно отказался от Indy и OpenSSL и использовал WinInet для загрузки. Вот код, который работал для меня:
function Download(URL, User, Pass, FileName: string): Boolean;
const
BufferSize = 1024;
var
hSession, hURL: HInternet;
Buffer: array[1..BufferSize] of Byte;
BufferLen: DWORD;
F: File;
begin
Result := False;
hSession := InternetOpen('', INTERNET_OPEN_TYPE_PRECONFIG, nil, nil, 0) ;
// Establish the secure connection
InternetConnect (
hSession,
PChar(FullURL),
INTERNET_DEFAULT_HTTPS_PORT,
PChar(User),
PChar(Pass),
INTERNET_SERVICE_HTTP,
0,
0
);
try
hURL := InternetOpenURL(hSession, PChar(URL), nil, 0, 0, 0) ;
try
AssignFile(f, FileName);
Rewrite(f,1);
try
repeat
InternetReadFile(hURL, @Buffer, SizeOf(Buffer), BufferLen) ;
BlockWrite(f, Buffer, BufferLen)
until BufferLen = 0;
finally
CloseFile(f) ;
Result := True;
end;
finally
InternetCloseHandle(hURL)
end
finally
InternetCloseHandle(hSession)
end;
end;