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In 1977 researchers and MIT described what asymmetric algorithm?
Public keys
https://en.wikipedia.org/wiki/Public-key_cryptography
Public-key cryptography, or asymmetric cryptography, is a cryptographic system that uses pairs of keys: public keys, which may be disseminated widely, and private keys, which are known only to the owner. The generation of such keys depends on cryptographic algorithms based on mathematical problems to produce one-way functions. Effective security only requires keeping the private key private; the public key can be openly distributed without compromising security.
In such a system, any person can encrypt a message using the receiver's public key, but that encrypted message can only be decrypted with the receiver's private key.
Alice and Bob have two keys of their own --- just to be clear, that's four keys total. Each party has their own public key, which they share with the world, and their own private key which they well, which they keep private, of course but, more than that, which they keep as a closely guarded secret. The magic of public key cryptography is that a message encrypted with the public key can only be decrypted with the private key. Alice will encrypt her message with Bob's public key, and even though Eve knows she used Bob's public key, and even though Eve knows Bob's public key herself, she is unable to decrypt the message. Only Bob, using his secret key, can decrypt the message assuming he's kept it secret, of course.
Alice and Bob do not need to plan anything ahead of time to communicate securely: they generate their public-private key pairs independently, and happily broadcast their public keys to the world at large. Alice can rest assured that only Bob can decrypt the message she sends because she has encrypted it with his public key.