Zero Knowledge

Published: Sun Jan 23 2022

💕A Valentines Mystery💕

In the spirit of the season, I thought I might share a festive take on a complex topic.

At first pass, the idea of sharing a secret🤫 without actually sharing the secret seems a bit overwhelming. Hopefully, We can help a couple of kiddos figure out if they got the same number of valentine cards in their boxes.

Tom👦 and Jane👧 both think they are the most popular kiddos in school. Being kids, they want to avoid being embarrassed if they didn’t get as many cards as someone else. How can they tell if they got the SAME NUMBER of cards without giving away their secret?

In this story, to keep things simple, friends can only give each other 10, 20, or 30 cards for Valentines. No more, no less. (In reality, this could be any number.)

Jane devises a method to learn if she and Tom have received the same number of cards.

She sets out three separate boxes 🗳 each with a number on them. She locks the boxes and throws away all but one 🗝 key! This step is, well, key to the security of the whole operation.

Now Jane only has access to the box which represents the number of cards she has. She ended up with 30 cards!

Jane leaves the room and Tom enters.

Tom has three pieces of paper with him. One with a ✅ and two with ❌s. He places the ✅ paper in the box labeled 20. He then places the ❌s in the other two boxes and heads out of the room.

When Jane returns, he opens the 30 box and finds the ❌ paper.

She takes the paper to Tom and they both know that they have different numbers of cards, but neither of them knows how many the other has received.

They have proof that their numbers differ, while having no knowledge of the number of gifts they each have.