Estrin's scheme
Imagine you have a secret that you want to keep safe, like your favorite toy or candy. You want to make sure no one else can find it or take it away from you. This is the same goal as someone who wants to keep their important computer files or messages safe from other people.
Estrin's scheme is a way to make sure that only the person who is supposed to have access to these secrets can see them. It works kind of like a puzzle that only the right person can solve.
Here's how it works:
First, imagine that you have a big box of numbers like this:
5, 9, 12, 8, 3, 18
If you wanted to keep this box of numbers safe, you could use Estrin's scheme to protect it.
You would start by dividing the numbers into two groups:
Group 1: 5, 12, 3
Group 2: 9, 8, 18
Next, you would pick a secret number, like 7, and add it to each of the numbers in Group 1. So now Group 1 looks like this:
12, 19, 10
Then, you would subtract that same secret number (7) from each of the numbers in Group 2. So now Group 2 looks like this:
2, 1, 11
Now comes the puzzle part. You take these two groups and add them together like this:
12 + 2 = 14
19 + 1 = 20
10 + 11 = 21
So now you have a new set of numbers:
14, 20, 21
But this set of numbers is still a secret, because it can only be unlocked with the secret number (7) that you used at the beginning. If someone else tried to solve the puzzle without the secret number, they wouldn't be able to get the same set of numbers.
The person who is supposed to have access to the secret set of numbers would know the secret number (7), so they could solve the puzzle and get the original box of numbers (5, 9, 12, 8, 3, 18).
This is just one example of how Estrin's scheme can be used to keep secrets safe. It's a clever way of using math to create puzzles that only the right person can solve.
Estrin's scheme is a way to make sure that only the person who is supposed to have access to these secrets can see them. It works kind of like a puzzle that only the right person can solve.
Here's how it works:
First, imagine that you have a big box of numbers like this:
5, 9, 12, 8, 3, 18
If you wanted to keep this box of numbers safe, you could use Estrin's scheme to protect it.
You would start by dividing the numbers into two groups:
Group 1: 5, 12, 3
Group 2: 9, 8, 18
Next, you would pick a secret number, like 7, and add it to each of the numbers in Group 1. So now Group 1 looks like this:
12, 19, 10
Then, you would subtract that same secret number (7) from each of the numbers in Group 2. So now Group 2 looks like this:
2, 1, 11
Now comes the puzzle part. You take these two groups and add them together like this:
12 + 2 = 14
19 + 1 = 20
10 + 11 = 21
So now you have a new set of numbers:
14, 20, 21
But this set of numbers is still a secret, because it can only be unlocked with the secret number (7) that you used at the beginning. If someone else tried to solve the puzzle without the secret number, they wouldn't be able to get the same set of numbers.
The person who is supposed to have access to the secret set of numbers would know the secret number (7), so they could solve the puzzle and get the original box of numbers (5, 9, 12, 8, 3, 18).
This is just one example of how Estrin's scheme can be used to keep secrets safe. It's a clever way of using math to create puzzles that only the right person can solve.