Hi folks, Ed Amoroso here.

Now we've spent a lot of time in videos looking

at conventional cryptography, conventional encryption.

But one thing we haven't looked at that's kind of a fatal problem,

but we'll see in a minute it's not totally fatal but it seems fatal,

to conventional cryptography is that it doesn't scale.

And rather than just whip an equation at you,

which is the way it was always explained to me,

I want to show you kind of we'll build a progression of the problem and you'll see.

Let's say, you and I are together and we want to be able to do cryptography between us,

we want to use conventional cryptography.

So, how many keys do we need? One, right?

You and me, one. Now let's say a new person joins us.

So then we have three people, okay?

We have three participants.

What we need now, it turns out are three shared keys, right?

So, there's a little bit of extra work now.

Somebody joins us, we have one,

you have one, I have one.

Now let's say a fourth person comes,

and we're four participants.

Guess what, we need six shared keys.

That doesn't sound great, right?

You can see the drawing,

as we build the drawing here. This is not good.

It seems like the amount of work to add a participant is growing.

Get to five participants,

you need 10 shared keys.

And guess what, when you get to six participants,

you need 15 shared keys.

So the amount of work it took to add

the sixth participant is

five times the amount of work that was required to add the first,

two, you know, so we had two.

That's not good. That suggests that if you got

a big auditorium full of people and people in the room,

and then somebody comes in and wants to be part of

the- we're all set up where we've got mutual shared secrets,

shared keys between all of us.

If the n+first person comes in,

then that person has to do a secret with all n us.

And you can see that that's not a great thing.

That's why when you go to buy something on amazon.com,

the scheme doesn't involve, oh,

you want to be able to buy from Amazon,

oh I have to somehow have a secret,

we have to give you a key, your personal private key with Amazon.

That's crazy. That's not going to work. That wouldn't be scaled.

If we had stuck with this scheme as the basis for cryptography on the Internet,

we wouldn't have companies like Amazon.

Now, I do want to say,

conventional cryptography is amazingly efficient, it's amazingly efficient.

We won't want to throw out the power of block encryption,

chained block encryption in multiple modes.

That we want to keep. But the question is,

can we come up with a way to scale it?

And in computer security, cyber security,

we've had a few incredible contributions,

but the solution to this problem,

the solution to the scaling problem in conventional cryptography in such a manner that

allows explosions of numbers of people that can use cryptography to buy and sell,

and interact, and build communities,

and build businesses, has been one of the great contributions of computing to our world.

This is almost like the invention of the printing press.

Our next few videos are going to take you through

a technology that has changed your life,

my life and everybody you know.

It just has changed the world by solving this problem namely,

the scaling problem for conventional crypto,

but somehow keeping the efficiency of

cryptography so that we can do things very quickly using efficient algorithms,

but in a way that doesn't require a third party

to adjudicate or arbitrate in the middle of the protocol.

So I want you just for additional consideration,

why don't you take some time,

see if you can whip up a little mathematical equation for the scaling.

If you can't find it,

you can look it up it's actually very simple.

But think about the equation of how you go about adding and scaling

up cryptography and you'll see that it's not going to be very

conducive to the kinds of things we're going to want to do on the Internet.

So, the next video will introduce the basics of public key cryptography,

of public key infrastructure, PKI.

And I'll tell you a little bit about some of the people who are

involved in introducing it to all of us.

So I look forward to seeing in the next video.