Honestly if you figure it out, someone else is probably already on the verge of figuring it out or already has and is probably going through the same question. Likely a major intelligence power is ahead of you. There's very likely no benefit to keeping it to yourself for any significant amount of time and a lot of risk.

Just publish it. At most demonstrate it's been broken in some incontrovertible way so people figure out next steps more quickly. Protect yourself as best you can.