Name: AES解釋 (高級加密標準) - Computerphile (AES Explained (Advanced Encryption Standard) - Computerphile)
Uploaded: 2021-01-14T10:14:43.000Z
Duration: 14 min 14 s
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基礎被動語態

Let's delve into a s and talk about you know what's good about it, how it works and why it was judged good enough to be the advanced encryption standard.

Okay, so in that perhaps slightly infuriating way I manage should not say anything about how it works.

In the last video, it'll let's start with a few numbers that we briefly mentioned in the last video.

That means it takes 128 bits off message on encrypted into 128 bits off cipher text.

Now that key cannot ever be 128 192 or 256 bits on DDE.

That gives you just varying amounts of security.

If you if you find your brows using 128 bit, that's okay.

These were specified as part of A s standard.

But I just think that we're taking 16 bites at 128 bits and we're doing something to it that turns it into some cipher text.

And because this is an SP network, we're gonna be doing some amount off substitution or could bring in some confusion on some amount of permutation moving things around to add diffusion you don't want just like the Enigma Machine.

You don't want to have one bite in one bite out, because that's gonna be easier to analyze on in.

Instead of having a long line of of bites, orbits like most Cyphers might arrange things.

So we have our message, which is 128 bit.

Every time I try and do a grid, it always goes well.

So bite naught is going to be in here on bite one and bite to and by three and then 45678 column major order.

So actually what we're doing is we're taking our 128 bit message and we're just laying it out in this order like this on dhe.

Then we're going to start doing RSP network gonna commute.

We're gonna substitute bites and then we're gonna transform it into some way where an attacker can't read what the message used to be.

So there are a few different operations that A s will do but remember, But everything in a s happens on this four by four grid.

Remember, we got the SP network, we're gonna have a substitution permutation, and we're gonna add darkie and as well at some point.

We're going to first bring in a part of our key on within a performing excell operation we named Member.

We put in all K intermediate between the rounds to battle secrecy rest.

Then we're going to do all round, so that's gonna be substitute bites.

Then we're going to shift rose on their finally, we're going to mix columns on dhe.

This is gonna be our substitution, and this is gonna be our permutation.

And finally at the end of each round, we're going toe out our ki add around key like this, and then this is going to be one around.

And the only thing to mention is that the mixed columns is in all around except the last one.

Because this permutation has no effect on the last round.

The output doesn't make it doesn't make any difference.

So it's exactly like this, except for this one, is missing on the lost ground.

When you've got 128 bit key, you have 10 of these rounds.

When you have 192 bit key, you have 12 of these rounds on.

When you have a 256 Vicky, you have 14 rounds.

But in a world of regard for exactly the same, so this is also an ex or down here add round key.

What we do is we take the original key, and as I mentioned in the SP Network video, we expand it using something called a key schedule into different round keys.

Perhaps this will be key one key to and so on, depending on which round we were in.

And so there'll be a key that's expanded for every round.

We weren't talking too much detail about the key.

Mainly it just takes your your shorter key on expands it sufficiently such that you can put it in a different rounds.

This is a much, much, much better version.

I mean, I can't stress this enough a much, much better version than the one I designed or showed in my SP network video.

We're substituting, and then we're gonna commute, and then we're gonna mix in our bounty on.

We're gonna do this over and over again until we have a cipher text.

So I guess the question then becomes what happens here, here and here off interest?

What's particularly nifty for me about yes, is that it doesn't use the same kind off operations that you might expect so X or, of course, happens everywhere in cryptography.

But actually, all of the operations within A s are essentially mathematical operations.

Our fields in his read Solomon video on the answer is by using Gallo our fields theory over finite feels and doing lots and lots of long divisions on traditions for a finite field or gal.

Our field, which are interchangeable names they What you have in the field is you have some some number of elements.

So let's say all the numbers between Norton 10 for example, and you have different operations, you can perform on that field.

So in mind are we have a gala Warfield off to to the Eight Elements.

And then in this field, weaken do addition, subtraction, multiplication on dhe division or extra two minus one inversion.

The important thing to remember about final field if we don't go any further with the math at all is that to ta elements is a bite, right?

So each element in this callow a field is just a bite.

So we start with north North Lord Lord Lord Lord, Lord Lord, we go away.

211111111 And so there are 256 off these elements in this particular finite field.

The one take home message that you need to know about this even if you don't ever look at it again, is that whichever of these operations we do?

We produce another element in this field.

We never under flow and go into negative numbers, anything.

There's no float representation, anything like this.

If we take one of these numbers and we add them to another one, we find a different one.

And if we multiply them or inverse invert them or divide, we go to a different one.

Which makes it quite nice for imprinting a cipher because a lot of these have an opposite.

So, for example, addition and subtraction under each other, modification and inversion or dividing, they undo each other.

If we've got our four by four by representation of our data path in A s.

We can perform informations on here within this final field and by the end will still be in the final field.

We won't have gone over to 130 bits 140 bits or somebody's officer like that.

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