Trunks and padlocks without shared key

1. The open (keyless) lock looks like a public key: anyone can use it to lock/encrypt.
2. Analogy with current cryptography: n=pq is published as part of the public key.
3. Answer (3-trip protocol): You add your lock B (A+B remain) and return it to me.

Answer (3-trip protocol):

1. I put the message in the trunk and close it with my A lock. I send it to you.
2. You add your B lock (A+B left) and return it to me.
3. I remove A and send it back to you (only B remains).
4. You remove B and read the content.

In no section does the trunk travel open.
Analogy with current cryptography:

• The open padlock (without key) looks like a public key: anyone can use it to lock/encrypt.
• The key of the padlock looks like the private key: only the owner can open/decrypt it.

What role does the prime number have?
In RSA there are no physical locks: there is modular arithmetic.

• Large cousins ​​$p,q$ are chosen.
• $n=pq$ is published as part of the public key.
• Safety depends on the difficulty of factoring $n$ to recover $p,q$.

Important: it is not identical to RSA
They are conceptually similar, but different:

1. The trunk protocol uses round trip (multiple steps); RSA allows single-send encryption with the recipient's public key.
2. The trunk involves a physical operation of “removing my lock, leaving yours”; In cryptography this is formalized with mathematical functions.3. In real systems there is authentication and signatures to prevent impersonation (MITM), something that the puzzle simplifies.

Conclusion: It is an excellent insight into asymmetric cryptography, but not a complete modern cryptographic protocol.