# Principle of asymmetric algorithm in plain english

I was giving a presentation to my colleagues about cryptography basics in which I explained about asymmetric algorithm and its use. One of the common question from the audience about asymmetric algorithm encryption/decryption is, why can't we decrypt the cipher data using the same key(e.g. public key) that we've used to encrypt(like symmetric algorithm). I know it is the mathematical property that prevents this but I really don't know how to explain in plain english. The question is more like if we do "10 + 2"(assume 10 as plaintext and 2 is key) then why can't we do "12 - 2"(12 is ciphertext and 2 is encryption key) to get the original data.

Can anyone help me to explain the principle of asymmetric algorithm in plain english?

-

It's like one of these:

Say you want to secure something in a box. Anyone can close the lock (public key). This means anyone will be able to put something into the box and lock the box (they won't be able to open the lock once it's locked (you just pinch these closed)). The key to open the lock is something only you have (private key). You are the only one that will be able to open the lock and see what's inside the box.

I suggest you buy on of these to demonstrate how they work.

-
Great analogy! I'll have to steal this for future use... – Polynomial Nov 23 '12 at 7:14
If you were to rename "public key" to something else (and the world adopted that language) what would you call it? A "shared lock"? "Shared lockbox"? – LamonteCristo Nov 28 '12 at 3:37
With the little difference that public need a so-called `public key` to close the lock. ;-) – F. Hauri Dec 30 '12 at 12:28
Just change in your mind "public key" by "public lock", it will help :) The private key can unlock things locked by the publick lock (ie, the private key can decrypt things encrypted by the public key). (Same thing as in the answer, I just re-read it ^^ I wonder if the term "public lock" could become standard, it would be so much easier to grasp a "public lock / private key" uses and capabilities) – Olivier Dulac Jun 6 '13 at 12:26
I'm not ok with this: For closing a lock, there is no need of a key! While using a public key is using a key! Your analogy is more adapted to operation like umount and forgot masterkey of a encrypted filesystem. – F. Hauri Dec 3 '13 at 23:01

I found these videos easy to understand and usefull:

The second is starting with SSL, but later the guy is speaking about symmetric and asymmetric cryptography:

-
That first link is really good for explanation this in plain english :) – Chris Dale Nov 28 '12 at 6:49

This type of encryption relies on the simple fact that some things in life are easy to do in one 'direction' and very very difficult in the other 'direction'. For example, jumping from the top of a steep cliff into the sea below. This is easy. However, climbing out of the sea to the top of the cliff is very hard.

In mathematics we also have things which are easier to do one way than the other. For example. If I asked you to work out 6 x 6 x 6 thats basic multiplication. If I asked you to find the cube root of 216 this is less easy.

Asymmetric encryption takes advantage of a mathematical procedure which is easy to do one way but hard to do in reverse - unless you have the private key.

-

In addition to the great answer by @Lucas, you can make the comparison:

Symmetric cryptography is like a door lock. Everyone that has a key can lock and unlock:

Asymmetric cryptography is like a common lock or handcuff. Anyone can lock it but only the (private) key unlocks it:

-
You are contradicting me. Also anyone can have the key to the handcuffs as well and anyone can lock them as well. -1 for no real added value. – Lucas Kauffman Nov 28 '12 at 5:33
That's a lot better +1 – Lucas Kauffman Nov 28 '12 at 7:23

I've drawn this using XFig, approx in 2002.

Where `symetric` use same key for in and out,

while `asymetric` use different (incompatible or unexchangeable) keys.

Of course, this is schematic! In this drawing, there seem easy to built a reverse key! In cryptography, there come funny things like prime quotien making this operation (near) not possible.

Hope this help... (Nota this stuff is licenced under LGPL V2)

-
best answer for me :) – Akam Jan 30 '13 at 20:13

Just to blatantly steal Lucas's basic premise, which is excellent, and build a full narrative around it:

Symmetric cryptography is like a lockbox, such as a small fireproof safe. A key is required both to lock and to unlock the box, and the same key does both things. If you and I both had the key to one of these lockboxes, we could exchange secret messages or other valuable objects with each other, without anyone else being able to access whatever's in the box. We could even mail the box back and forth to each other, and nobody who handles the package in transit would be able to see what we're sending inside it.

However, what if you went out and bought a new lockbox, with two keys, and you needed to give me one of the keys to set up this method of exchanging messages? Well, one option is for us to meet in person and for you to physically hand me one of the keys. In computer parlance, that's an "offline key exchange", and it does happen in certain circumstances.

But what if I were on the other side of the world? It would be expensive, and impractical, for you to fly out to me, or vice versa, to physically exchange keys. Your only option is to mail me the key. But mailing me something in an ordinary envelope or box isn't secure; theoretically, someone could open the envelope or the box, get the key out, make a copy of it, then re-package the key and send it back on its way. Once that's been done, we're not the only two people that can see the contents of the lockbox that we'll be exchanging things in later, and so the keys, and the lockbox, aren't secure. And you can't send me the key in a lockbox, because then we're back to square one; I don't have the key to the lockbox that you'd use to send me the key to the lockbox.

So instead, I send you a padlock. The package containing the lock has my return address and a postmark from my local post office, and the padlock's engraved with my name, so you know it's from me. The padlock also has a serial number on it that was engraved by the store that sold me the lock, so if you had any doubts, you could call the store and they could verify that the padlock you got was given to me by them.