Is there any PHP function that encodes a string to a int value, which later I can decode it back to a string without any key?
Sure, you can convert strings to numbers and vice versa. Consider:
$a = "" + 1
gettype($a) // integer
$b = "$a"
gettype($b) // string
You can also do type casting with settype().
If I misunderstood you and you want to encode arbitrary strings, consider using base64_encode() and bas64_decode(). If you want to convert the base 64 string representation to a base 10 integer, simply use base_convert().