In 1976, a breakthrough idea for public key cryptography was conceived, solving the problems of secure communication and identity verification without physical interaction. The concept involved using a 'safe' with a mail slot for encryption and another party holding the keys for decryption, guaranteeing the sender's identity. This breakthrough by Whit led to the need for 'mathematical safes' and one-way functions to transform and protect information, where multiplying is easy but factoring is hard. This posed the groundwork for the development of public key cryptography.