# Explaining RSA to the people

Alright so I have some understanding of encryption and how it works. I was trying to explain it to my friend and a few others I couldn't at the time. I later came up with an analogy.

How accurate is this without getting too in depth

Dale, Sam, and Max are all sitting in a class room at their desks [Dale]---[Sam]---[Max]

Dale wants to send a message to Max. Max knows this so he takes a pencil and breaks it in half handing Dale the tip so he can write the message. Max then keeps the eraser. Dale is to far away to send his message to Max so he has to send it through Sam. Dale doesn't want Sam to read the message. Dale writes his message "Hi Max" he also takes 2 random letters and mixes them in with his message so it reads "qMaxHiD" he then passes the message to Sam to pass to max. Sam then passes the message to Max. Max's special eraser only erases the random letters. So that he can read message." Max would like to reply but he only has an eraser so he can't. So Dale takes a pencil and breaks it in half and sends the tip to Max so that he can send his message.

From Sam's perspective he sees a bunch of random letters "qMaxHiD" he tries to read the message by scrambling the letters until he reads "Hi Max" since their aren't many random letters it's fairly easy for Sam to do this. there are only 5,040 combinations this will take some time for max to do but if he can 100 combinations in a minute it will take Sam about 50 minutes to read the same. Knowing this Dale could add one more random letter bringing the possible combinations to 40,320 taking Sam 6.72 hours to read and making it so the Max only has to erase one more letter. Encryption works because it's easy to erase one letter but really hard to go through all the combinations.

-The pencil is the keypair -Sam is both the internet the message travel through and uncle same trying to read it -Having a bigger pencil with more lead allows you to write more random letters to mak

Does this analogy work. Could I improve on it.

How about this (and, at this level, it's not specific to RSA, but is equally analogous to any public key encryption method):

• Max makes a safe with a slit on the top. Max made the safe, so he knows the combination, but no one else does. He gives the safe to Sam, who gives it to Dale. Dale writes his note, and inserts it into the safe. He gives the safe back to Sam. Now, Sam can't open the safe, so he gives it to Max. Max uses his combination to open the safe and read the note.

The nice thing about this analogy is that it captures some of the real concerns from a straight-forward use of public key crypto:

• How does Dale know that the safe he was handed was actually made by Max? That's quite valid, and is also a concern with public key cryptography.

• What if Sam inserts his own message into the safe? That's also a valid concern with public key crypto; as designed, Max has no way of knowing who wrote the message.

Both of these can be addressed, however that's a deeper topic.

(And, I'm pretty sure I read this somewhere, but I don't remember where...)

• I've used the same basic idea with a combination lock Apr 30, 2020 at 20:58
• The big issue I have with this (and the scheme in the question, and most explanations of public-key crypto) is that it covers direct encryption of a message. But it doesn't cover signatures, it doesn't cover KEMs, and it doesn't cover DH-style exchange. Yet those things are what public-key crypto is actually used for, not message encryption! Apr 30, 2020 at 21:11
• I am trying to show why crypto is so important. And what makes it different a coded message. A black box I feel like doesn't really explain why it's secure Apr 30, 2020 at 22:16
• @SAIPeregrinus: one problem coming up with an analogy to a public key signature system is that there doesn't appear to be anything in the real world that acts quite like a signature - not even a signature (!). After all, if you have a signed piece of paper, you could attempt to modify what the paper said without modifying the signature - you can't do that (or so we hope) with a public key signature. May 1, 2020 at 20:57
• @poncho true, but going from an inability to convey the uses of signatures by analogy to describing asymmetric crypto as being used for message encryption is a stretch. Arbitrary asymmetric message encryption is possible, but it's quite rarely a good idea, and isn't done in any of the common cryptographic protocols. May 4, 2020 at 13:33

I thought of an example based on something that happened years ago:

We give the sender a blank jigsaw puzzle on which they draw their message. The then "encrypt" the puzzle by breaking the pieces apart and putting them in a bag. Now suppose that before sending them the puzzle, we number the back of each piece with invisible ink. So the user (or anyone trying to intercept the message) attempting to read the message would have to assemble the puzzle normally (difficult). But when we "decrypt" the message, we know about the invisible ink numbering, and can use that to assemble the puzzle and flip it over to read the message (not trivial, but much easier).