Absolute encryption (one-time notepads)

Hello friends!

Today we will talk again about cryptography. But now we will tell you something that truly surprises you. Do you think that any cipher in the world can be hacked?

Here, for example, take from past articles the famous RSA encryption method that ensures the security of the entire Internet. For hacking, it just requires space computing power - and yet, theoretically, it can be hacked in a very long time. Especially if people invent quantum computers - with almost unlimited computing power.

And yet, if you imagine that quantum computers are created and the computing power becomes infinite - will there be at least one way to still securely encrypt information?

The answer is yes, there is such a way. And it is called Absolute Encryption or one-time Notepads. And surprisingly, it is even easier than RSA. Even an elementary school student can understand it.

Consider the following scheme (at the end of the numbers in brackets we write the remainder of division by 2: so for odd numbers, the remainder when divided by 2 = 1, for even numbers = 0)

even (0) + even (0) = even (0), example 4 + 6 = 10

odd (1) + odd (1) = even (0), example 3 + 7 = 10

odd (1) + even (0) = odd (1), example 3 + 6 = 9

even (0) + odd (1) = odd (1), example 6 + 3 = 9

It turns out this arithmetic of addition of residues from division by 2:

0+0=0

1+1=0

1+0=1

0+1=1

Now imagine that our message that we want to encrypt and transmit - consists of 0 and 1, for example

0 1 1 1 0 1 0 0 1  - this is the original message

To encrypt take a random set of 0 and 1, equal in length

encrypted message - we will call this set a one-time notepad:

1 0 1 1 0 1 0 1 1 - this is a one-time notepad

And make the addition operation in columns in the arithmetic of the residuals

0 1 1  0 1 0 0 1 - this is the original message

1 0 1  0 1 0 1 1 - this is a one-time notepad

_____________

1 1 0  0 0 0 1 0 - This is an encrypted message. 

And now attention - how can you find out about this message, which message was the original one? The answer is no way !!! - If you do not have a one-time notepad.

Indeed, in the first position of the encrypted message is 1, from which it could come in the original message? From 0, if the notebad was 1 (as in the first column). From 1, if the notepad was 0 (as in the 2nd column)

In the third position of the encrypted message is 0, from which it could turn out in the original message? From 1, if the notepad was 1 (as in the 3rd column). From 0, if the notepad was 0 (as in the 4th column)

That is, once again - in an encrypted message, 0 could come out of anything (from 0 or 1 in the original message) - it all depends on the notepad, and 1 could come out of anything (from 0 or 1 in the original message) - everything depends on the notepad

That is absolutely any set of 0 and 1 could be a prototype of an encrypted message - in which absolutely any information could be encrypted! It could be equally as top-secret data, and poems of the famous poet.

To decrypt a message — you must do the opposite — again, apply a one-time notepad to the encrypted message — and you’ll get the original message:

1 1 0  0 0 0 1 0 - This is an encrypted message. 

1 0 1  0 1 0 1 1 - this is a one-time notepad

_____________

0 1 1  0 1 0 0 1 - this is the original message

This encryption method is impossible to crack in any way, if you do not have an encrypting and the same decrypting notepad.

Notepads are called one-time, because for security purposes it is recommended to use a new notepad for each new message.

So why, then, use RSA in Internet encryption? One of the main reasons is that notepads should be as long as encrypted messages. This leads to traffic overspending. While in RSA, even 100-digit prime numbers are relatively small compared to the huge amounts of traffic transmitted on the Internet. And besides, absolute encryption is symmetric encryption - the same notepad (key) is used for both encryption and decryption of a message. RSA is a rare example of asymmetric encryption — where encryption and decryption keys are different — and this is more efficient. But this is a topic for individual articles.

And nevertheless - all these in no way detract from the fact that messages encrypted with one-time notepads cannot be decrypted in principle. No matter how powerful computers you use.