»Pulchinella's Secret«; »the secret of Mr. Punch«: an open secret. The idiom derives from a classic trope of the Commedia dell'Arte: the arrogant Pulchinella is entrusted with or believes he has a secret, but he blabs, or the truth is obvious; either way, everybody knows, and he is laughed at behind his back. Or, again, in a variant, Pulchinella spreads some tale, but tells everyone he tells it to that it is a secret; nobody admits hearing it to anyone else, and from that the comedy arises, similar, for instance, to the situation in The Emperor's New Clothes. From this variant it's occasionally argued that there is a difference between an open secret and a secreto di Pulchinella in that, although everyone knows the latter, nobody will admit it; but this is a case of hypercorrection, a construction of distinction between synonyms, as the phrase was not historically used that way.
Sometimes one sees the origin of this idiom attributed to a play by Pierre Wolff, Le Secret de Polichinelle, but this is entirely false; the play is from 1903, whereas Commedia dell'Arte originated in the 16th century (or arguably the 3rd century BC, with the Plautine comedy). Not even the French version of the idiom originates with Wolff; one finds it already in mid-19th century literature. (Indeed, the term »open secret« may be newer, being first recorded in 1828.)