Secret sharing by using just "private secrets"? TLS is using 3 way handshake. Isn't that possible to use such 3 way handshake protocol to share a secret without using a public key scheme, for instance as follows: Let A, B be private secrets of Alice and Bob respectively, where A,B  are elements in a commutative groups. Alice wants to share the secret X with Bob, and sends Bob AX. Bob multiplies it by his secret B to create BAX, and sends it back to Alice, that Multiplied it By 1/A, creating BX, that is sent back to Bob, that multiplies it by 1/B, getting X, the secret Alice wanted to share. Is there a principle problem with this scheme?
The attacker sees AX and BAX, and just divides them to compute B. Then they see BX and divide again to compute X.