As I'm sure you guessed, a generic claim of this sort will not suffice under New York law.
To the contrary, a New York County trial court recently articulated the rule, as well as its underlying rationale, as follows:
"[T]he law requires that a trade secret plaintiff identify trade secrets with reasonable particularity early in the case.See, Xerox Corp. v. IBM Corp., 64 FRD 367, 371 (SD NY 1974) ("[t]he burden is upon the plaintiff to specify [the alleged trade secrets], not upon the defendant to guess at what they are…Clearly until this is done, neither the court nor the parties can know, with any degree of certainty, whether discovery is relevant or not; and it is doubtful whether [defendant] can undertake a meaningful discovery program…."). Only by distinguishing between the general knowledge in their field and their trade secrets, will the court be capable of setting the parameters of discovery and will defendants be able to prepare their defense."
In other words, a plaintiff cannot be heard to claim on the one hand, that the defendant stole his confidential information, yet on the other hand refuse to identify what it is that the defendant stole.
Alternatively, "I could tell you, but I'd have to kill you" doesn't work in New York's courts.