I\'m looking for a simple clock synchronization protocol that would be easy to implement with small footprint and that would work also in the absence of internet connection,
Might Precision Time Protocol fit the bill? It doesn't look real simple, but it seems to do more or less exactly what you are asking for. (There are some open source implementations referenced on the Wikipedia page.)
I think the problem is that this is an inherently tricky problem, so the solutions tend to be complex. NTP is trying to provide a correct absolute time, which definitely goes beyond what you need, but it does have the advantage of being well known and widely implemented.