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A Stick Figure Guide to the Advanced

Encryption Standard (AES)

Sep 22, 2009

(A play in 4 acts. Please feel free to exit along with the stage character that best

represents you. Take intermissions as you see ﬁt. Click on the stage if you have a hard

time seeing it. If you get bored, you can jump to the code. Most importantly, enjoy the

show!)

Act 1: Once Upon a Time…

Moserware About

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Act 2: Crypto Basics

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Act 3: Details

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Act 4: Math!

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Epilogue

I created a heavily-commented AES/Rijndael implementation to go along with this post and put

it on GitHub. In keeping with the Foot-Shooting Prevention Agreement, it shouldn’t be used for

production code, but it should be helpful in seeing exactly where all the numbers came from in

this play. Several resources were useful in creating this:

The Design of Rijndael is the book on the subject, written by the

Rijndael creators. It was helpful in understanding speciﬁcs, especially

the math (although some parts were beyond me). It’s also where I got

the math notation and graphical representation in the left and right

corners of the scenes describing the layers (SubBytes, ShiftRows,

MixColumns, and AddRoundKey).

The FIPS-197 speciﬁcation formally deﬁnes AES and provides a good

overview.

The Puzzle Palace, especially chapter 9, was helpful while creating

Act 1. For more on how the NSA modiﬁed DES, see this.

More on Intel’s (and now AMD) inclusion of native AES instructions can be found here and

in detail here. - Other helpful resources include Wikipedia, Sam Trenholme’s AES math

series, and this animation.

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Please leave a comment if you notice something that can be better explained.

Update #1: Several scenes were updated to ﬁx some errors mentioned in the comments.

Update #2: By request, I’ve created a slide show presentation of this play in both PowerPoint

and PDF formats. I’ve licensed them under the Creative Commons Attribution License so that

you can use them as you see ﬁt. If you’re teaching a class, consider giving extra credit to any

student giving a worthy interpretive dance rendition in accordance with the Foot-Shooting

Prevention Agreement.

251 Comments Moserware

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•Reply •

Chandan Jha • 3 months ago

Wow! That was an awesome explanation. Thanks for the PPT and PDF... Good contribution...

Cheers!

PS: couldn't manage with the Maths part but still went through it. ;-) need to improve my

maths skills.

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•Reply •

Anonymous • 8 years ago

Should be be in the preface of CS cryptography textbooks! Terriﬁc

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•Reply •

Adam M. Erickson • 4 years ago

This should be in CS and ISM textbooks. A+ Moser.

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•Reply •

James McCune • 14 days ago

Awesome content man!

Really helped me out

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•Reply •

Leonard Michael Hurlocker • 2 months ago

Love it! Thx.

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Recommend

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•Reply •

Hope Ordu • 3 months ago

Lovely explanation. Couldn't have understood any better

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•Reply •

Matthew Ewer • 5 months ago

In the big chart, bottom right, in the bottom right of the Inverse Mix table, I think that B

should be an E.

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•Reply •

Lightning342 • 5 months ago

Great epilogue, I especially liked the math parts that visualize the operations. Just one issue;

in both encryption and decryption the last round is always the one with three steps (without

mixcolumns). Check the pseudo code in NIST.FIPS.197 (ﬁgure 5 & 12), or search the Internet

for images on "simpliﬁed aes decrypt" . So aes_act_3_scene_20_decrypting_1100 is

incorrect.

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•Reply •

Sleem A. Lama • 6 months ago

This is awesome.. Thank you

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•Reply •

ATA UR REHMAN • 10 months ago

Seriously One great article.. Loved it (Y)

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•Reply •

Rami Stefanidis • a year ago

Very cool article. Thank you

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•Reply •

Gidz Paul • a year ago

Awesome.. :o

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•Reply •

Walter Zambotti • a year ago

Very nice. Did I miss where in the presentation you display the ﬁnal encrypted text???

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•Reply •

netdeamon • 2 years ago

Cool !!! Keep it up!

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•Reply •

Felipe S Mattos • 2 years ago

this is rocksome! very nice work!

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•Reply •

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•Reply •

assignment writing • 2 years ago

It's actually a good work that you have shared which covers up some topics about that kind

of subject that was being tackled in school for those students who studies in the ﬁeld of

engineering. Through this, they can learn something that they will going to use as their guide.

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•Reply •

Benjamin Barenblat • 3 years ago

A minor error in act 3, scene 11: entry a₀₁ of the right block should read ‘fb’, not ‘f8’. (This

has already been corrected in scenes 12 and 13.)

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•Reply •

Kevin • 4 years ago

Thanks man!! :)

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•Reply •

Raymond Starkey • 4 years ago

Talent, talent, talent, talent. Art - must try harder.

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•Reply •

Theuns Alberts • 4 years ago

Brilliantly explained! And thanks for the eﬀort with the accompanied code.

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•Reply •

Todd • 4 years ago

Awesome. But where is the part where the NSA builds in a back door to circumvent all the

cryptology?

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•Reply •

Anonymous • 4 years ago

was fun........gr8.......learning it and signng the letter....

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Anonymous • 5 years ago

Can't ﬁgure out if ALL these have any relation at all with this one:

"The key to this encryption rule is given by two numbers n and r. The number n is chosen in

a very particular way: n is the product of two primes p and q. where n is the product of two

primes p and q. To encrypt x we just compute: y = x^r(mod n).

The decryption then works via a simple formula, analogous to the encryption: we compute

y^s(mod n).

Suppose we choose n = p * q = 29 * 37 = 1073. Let's take r = 25 with this choice of n and r,

the choice s = 121 is an appropriate decryption key...

The decryption illustrated on the previous page is possible because r and s have a very

special relationship. With p = 29, and q = 37, we compute:

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•Reply •

special relationship. With p 29, and q 37, we compute:

m = (p-1) * (q-1) = 1008 and then we have chosen r and s so that:

r*s = 25 * 121 = 3025 = 1 (mod m)..."

Link: http://web.math.princeton.e...

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•Reply •

otis root • a year ago

> Anonymous

That is RSA

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•Reply •

Cường Đặng Đình • 5 years ago

thanks very much!!!!!!!!!

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•Reply •

Trung Le • 5 years ago

That was a really good work you have done! Helped me a ton to understand AES in a visual

way. Keep it up!

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•Reply •

KF • 5 years ago

Thank you for your awesome job... really let me understand much. This is fun too. Appreciate

it very much.

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•Reply •

Jeﬀ Moser • 5 years ago

Thanks everyone for the kind feedback!

Anonymous: For details about being resistant to cryptanalysis, I recommend reading the

book but it's quite a bit more complicated than this comic. Perhaps try the Wikipedia page.

Regarding modes, Wikipedia's page on it is pretty good.

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•Reply •

Charulatha Jain • 5 years ago

Its an awesome presentation and quite helpful for beginners to understand the concepts.

Thank you for the awesome presentation.

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•Reply •

Anonymous • 5 years ago

This is one of the most superb explanations of AES I've ever seen. So easy to understand,

it's brilliant. But I'd love to know more about the resistance to cryptanalysis, I understand

what it is but I have no idea how AES resists it. Plus I'd like to know more about the various

"modes" you touched on!

In summary: encore!

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•Reply •

durdave • 5 years ago

Great! But I'm still left with the question "Will Ashley go out with me?" Maybe if I get a

Ferrari?

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•Reply •

Anonymous • 5 years ago

Superb. Keep it up Brother.

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•Reply •

Anonymous • 5 years ago

Amazing would be an understatement!

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•Reply •

naveregnide • 6 years ago

Hey! Just stopping by to say that this lovely comic really helped me understand AES a lot

more. Such a great sense of humour used in it too! Thanks!

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•Reply •

Jeﬀ Moser • 6 years ago

Thanks everyone for the kind feedback over the years.

Special thanks to txipxi for the Spanish translation.

Vincent: For details on how all S-Box values are calculated, follow along with the S-Box

demonstration section my example program and the f(x) and g(x) section as well. For even

more details, see how I implemented f and g. Note speciﬁcally how "f" is a multiply then an

add/xor. Each bit of the result of the multiply is obtained through 8 boolean multiplies/ands.

Hope that helps!

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•Reply •

Vincent • 6 years ago

Hi Jeﬀ, is it possible to show your working on f({18})={6a}? I have been trying to work out the

rotational matrix part but still getting the answer wrong. Did you sum up all the 8 rows of

multiplication before you XOR with {63}?

Is it possible can anyone show the working for multiple inverse for {58} is {18}?

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•Reply •

Krishnaprasad • 6 years ago

This is great.. lot of eﬀort to explain, very easy to understand!! awesome..

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Anonymous • 6 years ago

W d f l! G t k!

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•Reply •

Wonderful! Great work!

Makes understanding AES a lot of fun!

Genius!

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•Reply •

txipi • 6 years ago

Awesome!!!

My humble contribution to your great work, a Spanish translation:

http://www.slideshare.net/t...

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•Reply •

The Grey Man • 6 years ago

WOW. Thanks for the excellent, amusing and visual run down on AES.

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•Reply •

SherryL • 6 years ago

Wow, it's great to explain the AES this way. I've tried much to understand AES before I found

this. BRAVO! Thanks!

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•Reply •

Anonymous • 6 years ago

I would like to read more like this..it was a fun way of learning for an adult.

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•Reply •

Anonymous • 6 years ago

Thanks for this.

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•Reply •

Jeﬀ Moser • 6 years ago

20 box: It's a decent book if you want a very academic overview of AES. It was a bit too

academic for my tastes and was one of the reasons why I created this post.

If you're looking for a more hands-on/pragmatic understanding of AES, I'd recommend you

just read and understand the source code that I included with this post.

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•Reply •

20 box • 6 years ago

Is that book you recommended is good? I am considering buying it here in India but it is too

costly a book for Indian standards and is not available on local markets.. so have to buy it

from amazon or something.. but too costly..

Just want to know if it is worth $100 or not? as it would be the price for me including

shipping...

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•Reply •

Sandoval • 7 years ago

wow!

99.9% of comp professionals never can talk in simple English; BUT you've just proved that

you are the 0.1%!

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•Reply •

<Martani/> Fakhrou • 7 years ago

Totally awesome,

this is gonna help me in my crypto exam tomorrow :D

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•Reply •

arun • 7 years ago

hey man..a very well explained..good job..

well m also working on AES and m really a bad prograamer..My work is with Equivalent

Inverse Cipher have you worked on it...got nay code of it????It's really urgent......pls

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•Reply •

Viviana • 7 years ago

Thanks a LOT for this explanation!

I nearly had given up trying to understand AES when I found that..!

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Anonymous • 7 years ago

After reading this I am not sure if I successfully crypt-ed or decrypt-ed my knowledge about

AES.

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