It's much safer to just send the public key over whatever medium and then use an authenticated channel to verify the authenticity of said public key.
Cryptography is often not about "uncrackable" but about confidence in security over a foreseen interval.
On the 4th of June 1943 the details of Operation Neptune ("D-Day") were a priceless secret of the Allied Command, a break that allowed Berlin to know the plan could have resulted in the invasion force being expected by a heavily prepared and well-reinforced German defence. Those who made it back to England alive would have no reward for their efforts.
By the 7th of June 1943 plans for Neptune were a historical curiosity of little military value.
And I did mean Neptune, the Overlord plans would have remained valuable for several weeks as they included details of the immediate objectives in Normandy and how resupply would be done, Neptune was just the invasion and related actions.