a list compiled by Alex Kasman (College of Charleston)

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Digital Fortress (1996)
Dan Brown
(click on names to see more mathematical fiction by the same author)

In a final act of defiance, a young Japanese genius threatens to make public his "unbreakable code" if the NSA does not confess that it has been reading even encrypted e-mails. The heroine of the story is a mathematician at the NSA, but you also cannot help but root for the "villain", whose plan continues to unfold even after his death.

This particular page is, by far, the most visited page on this Website. This is a testament to the book's appeal, and the fact that it leaves people with questions they want to find answered on the internet. However, it means that this page has grown too long (with comments and arguments back and forth from site visitors) to be easily read. Therefore, with apologies to the people whose quotes are being cut, I am going to attempt to organize it. As of December 2, 2004, it is being completely revised and placed in a more reasonable order than merely the order in which the comments from site visitors were received.

The topics you can read about below are:

  • Do people like or dislike the book? (And are we allowed to have and voice these opinions?) Obviously, many people do like this book. It is a best seller, and some people have written in to say what they liked about it and to defend the book from criticism. Others, including myself, did not like the book. Some of these people who did not like the book argued that it is amateurishly written, but most complain about the logical and mathematical errors. Especially considering that this sort of criticism is the focus of this entire website, I think that such comments are welcome. Moreover, I think it is worth noting that even though some people can read a book about a mathematician and enjoy it even though the mathematical ideas make no sense, there are others who will find these problems to be an obstacle to reading and enjoying the book.

    Personally, I found the writing to be lame and the plot twists to be nonsensical. I was unable to enjoy the book or suspend disbelief long enough to feel like I was doing anything other than wasting my time. Consequently, I was unable to finish it. Apparently, this was a mistake because (as with other Dan Brown books), many of the most interesting plot twists later explain that the things I found so annoying at the beginning were not true. However, this only partially resolves the problem. Clearly, I (as a reader) and the characters in the book (who are supposed to be really smart) are supposed to believe these things towards the beginning of the book, and so their lack of believability still affects my ability to read and enjoy the book.

    Note Added February 25, 2005: I still get about 5 messages a week from people who insist that we cannot complain about the innacuracies in this book. They say "You don't understand, it is FICTION so it doesn't have to be correct." But wait. Honestly! Can you tell me that you cannot imagine reading novel in which some things that don't make sense bother you even though it is fiction. Here's an example. Suppose there was a book about a man who is the most popular basketball player in the NBA, he has advertising contracts for every sort of product you could imagine, a wife who is a fashion model and chapter 3 you learn the shocking truth. Unbeknownst to most of the people around him, it turns out that he is actually both autistic and paralized from the neck down. His mother covered up this fact when he was a child by home schooling him and moving his arms and legs occassionally when nobody was looking, and the hoax was continued by one of his teammates. Most of the rest of the book is told from the point of view of his wife who is shocked and saddened and considers asking for a divorce since he is clearly not the man she thought she had married. Now, perhaps a few readers would not be bothered by this and say "it's fiction...not a biology textbook". Perhaps a few others would consider this artful writing. But, I bet 90 percent of the people who tried to read the book would stop at that point and say "That doesn't make any sense. I'm not going to finish reading this piece of ****." All I'm saying is that this book was the same way for me and quite a few other people who read it. I'm perfectly okay with the idea that other people like the book despite this, I'm just tired of hearing people tell me that I'm not allowed to have been annoyed by the nonsense!

    But, hey, that's just me! Let's see what other people have to say:

    Contributed by Leslie Bailey

    My favorite fiction book with mathmatical content is "the curious incident of the dog in the nightime". By comparison "Digital Fortress" is written by someone with Special Needs.

    Contributed by Anonymous

    Digital Fortress falls victim to the ever so delicate balancing act between technical facts and made-up phrases (that try to convey technical meanings to the average reader) that has plagued books and movies alike for years. The author, while trying to pay justice to technical actualities, needs to keep the less technically inclined readers' interest at the same time not offend the technical readers by using terms like "tie-ins" or "kill code". As a professional in the IT industry, I find myself hoping that one day the right book or movie will find the correct balance and therefore shine because of this day I haven't found one that comes close.

    Contributed by Sapphire

    I loved the book and the use of the mathematical content i am an a level maths student and i thought the mathematics used are perfect for the book. Compared to some other books i have read with mathematical content in them Dan Browns book in my opinion beats all the major contenders.

    Contributed by Kathryn

    I thought the book was very interesting. I had problems with parts of it though because it seemed like Dan Brown went into "textbook mode" sometimes. He would say a term that most people wouldn't know and then he would give a definition of sorts that I thought he could have done a lot better.

    Contributed by Chip

    I fail to understand how Dan's novels always seem to end up the same way, an excellent concept, very good plot twists, ruined by lack of research and fundamental errors. I am prepared usually to suspend disbelief, but this book went over the limit, either by glaring technical inaccuracies or just plain making things up.

    Contributed by Anonymous

    "I appreciated the story. I am familiar with encryption techniques and enjoyed the ideas that were discussed. The concept of encrypting a code with an unbreakable algorithm and then challenging the world to break the code was very clever. It was also fun to think about who "guards the guards." It was an enjoyable weekend read!"

    Contributed by Vickie

    I hated this book (and finished it anyway out of curiosity). Instead of creating believable characters who do believable things, he twists them around and makes them do stupid things just so it all fits into the stupid plot. Case in point: Susan can't understand how somebody broke into her computer and aborted the tracer program. Somebody got her screensaver password? Excuse me--they are all cryptologists for pete's sake. How hard is it to crack their screensaver codes? Give me a break.

    Contributed by Fionn

    I am 13, and I have just finished reading Digital Fortress. As with other Dan Brown books (I have read them all), there is a lot of speculation over the accuracy of the major themes in the book. I have not yet read anything that explains explicitly what is inaccurate in this book (except for the mention of the non-binary 64 character thing), nor with any other of his books. Even if it is inaccurate, it is a very interesting starting point for anyone with an interest in code-breaking. This is a very good novel, even if it is not entirely accurate.

    Contributed by Igor Fedchunov

    I did NOT like the Digital Fortress at all.

    IMHO its literary quality is disgusting: look - main hero is linguistic genius, professor - and 6' tall athlete, main heroine is mathematical genius, and (!) hi-paid hi-level executive, and beautiful woman capturing male guard's dreaming gaze, etc. Of course they make passionate love - guess where? of course ! - in front of fireplace in a "manor" in smoky mountains. Looks like a high school attempt in fiction writing.

    As for the plot twists and rationale behind - to me the book looks like cheap work - if any work at all. The author wants action with gunfire in the heart of NSA. He (and any reasonable person) knows it is impossible because of tight security. Did he worked hard to imagine really smart twists to overcome security ? No, he just pretended there is no security at all, not even video monitoring, in the Crypto! and so on, and so on....

    Contributed by Trent

    Thoroughly enjoyed the book -- only had to suspend reality a little bit(*), and couldn't put the silly thing down for the last half of the book! A new author for my library. YAY!

    Contributed by Sam

    I'm 16 and I just finished this book about 30 minutes ago. Personally, I loved it. It was really intense at most points and hard to put down. I came here because I was sort-of in that mindset of the book.. and the end code is really simple so i agree with 'we are watching you', but I think that he could have put in something a lot more meaningful than that. I really enjoyed it and would recommend it to anyone who doesn't complain about every inconsistancy in works of fiction that they read.

    Contributed by Anonymous

    I am a 60 year old female application software engineer and have just finished the book. As a piece of fiction I really had fun with it as long as I suspended reality. I had the villan and key code figured out about half way through the book. As stated above, I couldn't believe a group of highly intelligent code breakers couldn't figure out the 'prime difference'. Oh well, it was fun and the Ultimate Code at the end was pretty simplistic. The biggest criticism (and this happens in too many books) is the hero is handsome, intelligent and cannot be killed while the heroine is beautiful, sexy, smart and needs to be protected........come on!

    Contributed by Amy

    The error in the inconsistency of Dan Brown'n novels comes from the fact that he sells his books based on the impression that he has researched fully and one is to openly recieve and believe the info he is clumping together and passing around at truth (the DaVinci code in particular has some very stark pitfalls, most that poorly reflect the Catholic Church). Though I cannot totally abandon his books as his writing style and suspense factor is great. I personally love all three books I have read despite the inconsistancies. Though I am growing tired of the abundance of consistancy between Angels and Demons, The DaVinci Code, and Digital Fortress, though I have not read Deception Point I can only guess there will be a beautiful, intelligent female lead, a tall, greek-like similarly intelligent leading man, a father figure (for the female) gone awry, an innocent with too much knowlegde that ends up dead and so on.... similar character types and flaws make for similar plots no matter how varied the theme may be

    Contributed by Reid

    It was the worst book I ever read. I am not going to complain about the incosistencies, but I am going to complain about how predictable the book was. Although I missed a couple of details such as the NDAKOTA anagram, I knew, pretty much, how the thing was going to end by the first hundred or so pages. I will never put down a book, and that is why I raced through it. I wanted it to end as quickly as possible so I could read the Da Vinci Code, which I heard was excellent.

    Contributed by Astronotus ocellatus

    This was Brown's first novel, so let's cut the guy some slack. Second, the book is fiction, Brown never claims his work to be real or 100% accurate. I am not a mathmatician or a computer programmer or a computer engineer, however, I do know about writing and for all those readers who claimed they hated the book and who just couldn't get over the programing inconsistancies, the mathematics, and the accuracy of the locations, this was not a text book teaching people about computer programming or about encryption, it was a novel, and for someone who appearantly does not know how to create characters or develoe plots it kept even the most critical and cynical of readers reading until the end. I don't know about the rest of you but I couldn't write a NY best seller if I tried. I assume that if Dan Brown can cause so many to have such an interest in his work as well as try so hard to decode his ultimate code, then he is a good writer. Too many of you were too rolled up in your own personal ego. Get over it, not everyone has to be as smart as you. When you publish a NY best seller on algorithms and mathematics I'll tip my hat to you.

    Contributed by Alex

    I think it is unfair to accuse critics of the book of being "rolled up in personal ego" or involved in an intellectual competition with the author. It is true that different people like different works of fiction (it is, after all, a matter of taste), but I think we all have this in common: if the story seems to make no sense or has too many inconsistencies, the reader will have trouble enjoying it. For instance, if the author seems to have trouble maintaining characterizations -- if the character's personalities change at random, not because of the intent of the author but because the author is simply not very good at characterization -- then the reader might find it difficult to BELIEVE in the book. One can also imagine an author who is not good at keeping a sensible plot. Similarly, once math and science are brought into a book as significant components, there are many readers who will be bothered if these are mishandled. I am one of these readers. If you are able to read the book without being bothered by the nonsensical mathematical aspects, that is fine with me. However, you ought to understand that for readers who know about and care about mathematics, this book makes as much sense as a book in which the characterization and/or plot are too stupid to be enjoyable. And, yes, we are not bestselling authors ourselves. However, this website is designed for people who know and are interested in mathematics. I suspect that those people will similarly find this book unpleasant or impossible to read, and it is the purpose of this website to provide them with that information.

    Contributed by John Fakan

    I'm an avid reader (at least 100 books per year) and a PhD physicist/engineer with a strong interest in codes and ciphers. I've worked and co-lectured (luncheon/dinner speaker) for a number of years with the late Dan T. Moore, a good friend and former member of the OSS/CIA and author of "Cloak & Cipher". I have friends who work for the NSA, and I've also read Brown's "Angels and Demons" and "The DaVinci Code".

    With this background I found "Digital Fortress" a bit of a challenge to read and enjoy. It was filled with many assaults on my credulity, and I had to grant Brown a great deal of poetic license to get by those situations. Brown definitely has a knack as a storyteller, but I wish he would spend less time editorializing and more time researching and crafting his scenarios. "Digital Fortress" could have been so much better!

    But, I am glad I read it. My "3=Good" evaluation for the literary quality does reflect my feelings about it. I will read more of Brown's works in the hope he matures as a writer.

    Contributed by Alex

    The quality of a book is a subjective, not an objective, measure. It depends, among other things, upon the interests of the reader. This website is intended to be for people who have an interest in mathematics as well as in fiction. Such readers seem to have trouble enjoying "Digital Fortress" because the whole plot makes no sense from a mathematical point of view. This does not mean that the book is objectively "bad", but it does mean that frequent visitors to this site probably will not want to read "Digital Fortress". Others who will simply ignore the mathematical aspects may well enjoy the book. This is the final word on these matters. I will not post any more comments on the debate of whether it is fair for us to complain about the mathematical aspects of this book.

    Contributed by Anonymous

    I'm not a mathematician, but a chemist (actually working as a programmer / analyst at present), so maybe I'm a little skewed, but the whole 238U, 235U, 239Pu thing seemed absurd. Before I was ever even interested in chemistry, I knew a whole lot about radioactive isotopes. When I first saw the list of "orphans" presented (on page 403 of the paperback), I knew that (although not at all representative of anything actually related to computer programming) it was a Cesarean cypher, and didn't even bother to write it out as I knew exactly where they were going. On page 406, I read the plaintext and knew in an instant how it was going to end (though I guessed 2 as the prime number between 239Pu [atomic number 94] and 235U [atomic number 92]--the whole 238U thing being absurd on so many levels as to make me want to strangle Brown), but seemed spellbound to subject myself to the remaining painful argumentation of all these scientists behaving like 4th graders (just single out Jabba to see what I mean) trying to figure out such a simple concept.

    Nonetheless, something about the book kept me reading past chapter 6 or so (whence I realized what direction the plot was going to go--downhill fast) and I don't consider it a waste of my time. Maybe there is a sort of morbid curiosity that just makes you want to keep reading to see how much worse he can distort reality?

    Contributed by Ken

    I KNOW it's just a novel! It's listed under FICTION in the library. But when you're teased with a concept into reading a book, and the concept is weak in its conception, you feel disappointed, even with the obvious and enjoyable excitement and fast pace written into the story. In The Grapes Of Wrath, a wine bottle's cork is pulled out on one page, but the cap is screwed back on a couple pages later. While this lends to casual discussions of topological impossibilities, there is not a mathematical reference in the book's title, and the work is not faulted as such for the error. In The Lord Of The Flies, one of the boys starts a fire with the lenses from his glasses, but that would be rather impossible since the boy suffered from myopia. But optics is not a prime factor in the plot.

    I found all of the little 'codes' and puzzles in The Da Vinci Code pretty easy to figure out, too. And some of the plot points seemed to be a bit of a stretch for me. But I was able to enjoy The Da Vinci Code from a purely literary standpoint in that it had an exciting plot that moved quickly and gave the reader things to think about. It was, after all, my first Dan Brown novel.

    Had I read Digital Fortress first, however, I may not have enjoyed The Da Vinci Code as much after detecting all of the similarities in the cryptographer heroine, the college professor hero, the electronically hidden villain, the unsocialized assassin killing people on the heels of the hero, etc., and seeing all of the half-baked concepts written into them. I have Angels and Demons to read, and I'm afraid I've heard that its plot, too, is very similar. I hope that Dan Brown, while obviously able to spin a good yarn, isn't stuck in a rut. That curse caused problems for both Albert Einstein and Stephen King after much more prolific careers.

    Contributed by The Bibliophile

    I went through most of the comments on this site. My summing it up would be '...predictable, corny and math based book with hardly any actual math in it ...' I think Dan Brown takes good subjects and plots and twists them into pretty bad books. In this case cryptography and the basic plot is quite a good subject from which any good thriller author could have made a really good book (e.g. Ludlum, Forsythe etc). Instead Dan Brown has messed it up. In case of 'Digital Fortress' I know who the villain is just a few chapters into the book (compared to Da Vinci Code in which I got it in the middle of the book). The formula is - Find out who the author is calling 'supportive, soft strong, best etc' other than the hero and the heroine and you know who the villain is. Works for Da Vinci Code too! Corny - Example: Megan pepper-sprays David and runs away. David calls her by name and she comes back and says,"Mister! How did you know my name ? I didn't tell you my name!" [EXPLETIVE DELETED]!! Sounds like its from a detective novel by a 10 year old. Dan Brown knows a handful of computing words, math words which he keeps using. He should do more research before he writes his next book, if he wants to make it believable.

    Contributed by Bob

    I have recently read Digital Fortress and have to admit i loved it. The ideas put forward in the book fascinated me. So much so that i started reading more on the fact behind the fiction. Initially, i first found out that there was no such thing as the Bergofsky Principle. I wasnt too upset, because this is a work of fiction, and a certin amount of license should be granted. Im certainly not in a position to say that people who know instantily that the ideas put forward are farsical, should not be annoyed, but i might suggest that this book may not have been aimed at these people. I think it makes a very entertaining read for those ignorant amonst us to enjoy it entirely at face value. I think the pointing out the innaccuracies in the book to those people not in the know, is akin to telling a 12 year old watching Star Trek for the first time, that Warp Drive and Wormholes probably dont work in reality the way they are suggested in the show/films. The greater picture here i think is that after reading the book and being entertained by it for the duration, it compelled me to read into the subjects of mathematics and cryptogryphy more. Admittedly, finding the bergofsky Principle was a fabrication was a little disappointing, but the amount of factual information i have uncovered having been spurred on by the book is amazing. Surely, in spite of his taking of certain liberties, Brown can only be commended for bringing a relativly exclusive area of the sciences to the masses ??

    Contributed by Dave Bowes

    Great book. I realised that NDAKOTA was an anogram for TANKADO the second i saw it and was expecting one of the characters to realise it on the next page, at least the next chapter, but the whole book????? I'm no cryptographer but that was childs play. Maybe the fact that I read DaVinci Code and Angels and Demons first might have helped me understand Dan's encripting and puzzles??!! His other books always kept me guessing and surprised me with a totally different answer but this one was very predictable. The amazing thing is it was still a fascinating read. Dan Brown is a GOD!!! but we wont create a false religion for him or destroy all his texts. ;-) The 'key' to reading Dan Brown is to allow your mind to go into overdrive and try to predict everything and then surprise yourself when you are no where near!

  • How accurate is the math/computer science presented in the book?

    I know that many people do not care about the mathematical aspects of the book if they enjoyed reading it. However, discussing the math in fiction is what this website is all about. And, unfortunately, from this point of view, the book falls a bit short.

    On the plus side, it's nice that Brown chose a female mathematician for a heroine, and nice that he brings the NSA to the attention of some readers. However, here are some of the things that bothered people:

    Contributed by Alex

    Even though it turns out in the end that there was no real unbreakable code, the reader (and a bunch of cryptography experts in the story) are supposed to believe in it at least for a while, but it makes no sense as described. The existence of the unbreakable code is confirmed when the NSA's super-powerful computer is unable to decode a sample message that the genius gave them. They don't seem to consider the possibility that he just gave them a garbled mess which cannot be decrypted. If they are so easily convinced, it would be very easy to blackmail the NSA. Moreover, the explanation of how the unbreakable code works either makes no sense or is beyond me. I don't see how it could ever be decoded, making it useless.

    Contributed by Igor Fedchunov

    can you imagine a (super)computer blasting because of overheating due to cooling malfunction? Oh, boy! Ok, let go straight to the crown jewel: we have got a foolproof encryption algorithm. Everyone wants to see it. But its description is encrypted! Great! Its encryption employs THAT algorithm, and you will never know the algorithm's sectrets unless you have the key.... wait a minute! When you enter the key - the encrypted file will open up, and THAT means that there is a program there that takes the key and makes the decryption - so we can look at the program code and get the algorithm from there ! One does not have to decrypt the file to get the algorithm !

    And the last straw - in author's view a 64-bit key is represented by 64 character string. AND it is implied that it is NOT a binary string. Now that is really gross. Probably the author did not do ANY research for his so-called-book. That's why I would call this book a [EXPLETIVE DELETED].

    Contributed by T. Rall

    The idea that a computer can brute force any encrypted text, without knowing the algorithm used, is absurd. Yes, they can brute force keys for known algorithms, but not for unknown algorithms.

    Contributed by Michael S

    Like all other books from Dan Brown, this is quite an suspending thriller, with some unexpected turns, but if you want to learn something about cryptography without reading a math book, Simon Singh or even Edgar Allan Poe is definitely a better read.

    Almost any information about cryptograhy given in the book is a bit screwed up. Most notably i think is, that there IS a simple unbreakable code, which is known since quite a while, the so called "one time pad". You just need a true random (dice, quantom noise...) sequence as key, that is at least as long as your text. Then you xor or modulo add your text with this key. The point is, that because the key is longer (or as long as) the text, there are as many possibilites for keys as there are for plain texts, so you will get every possible plain text with the given length when brute forcing the key (everything from AAAAAAAA..ZZZZZZZZ). And you don't know which one is right! Of course, you must use such a key only once, so a lot of key material must be exchanged.

    The second thing is, that time for breaking a code usually doesn't grow linearly with key length, as suggested in the book, but exponentially. An old 64-bit (actually 56-bit) DES can be broken with 10,000 PCs within 24 hours, but even if you would turn every single electron of the whole Earth in a computer that can do one AES-256 decryption and plain text evaluation per attosecond, it would still take a day do brute force an AES-256 encrypted text. Brute forcing a 512-bit (symmetric encoding) key is already well beyond the cosmologic limit, meaning that even if the whole universe would do nothing than breaking this code for as long as it lasts, it couldn't do it. So such a code can be considered "practically safe". Unless the quantum computer guys make progress (which I doubt). And unless there is some backdoor. And this is the one thing Dan Brown got right about cryptography: Never use a code you suspect or know having a back door!

    P.S.: For asymmetric encryption ( PGP... ) brute forcing time does also rise exponentially with key length, but not quite as steep as with symmetric encryption. For this reason key length between 1024 and 4096 bits are used there, while 256 bits key length is assumed to be sufficient for symmetric encryption.

    Contributed by Anonymous

    It says in the book that the encryption uses 'mutation strings' which I'm pretty sure were made up for the story. This is how he explains the code being unbreakable, we are supposed to assume that the code evolves and changes its own algorithm with time.

    Contributed by Alex

    Coming up with a way to turn plain text into unintelligble garbage is not a "code"...there has to be some way to turn it back into the original message. If the thing that makes the code "unbreakable" is that the code itself changes unpredictably from moment to moment, then I cannot imagine how anyone could ever decode a message that had been "encoded" in this way.

    Contributed by Marco Polo

    It would seem that almost everyone has missed the point of the story.

    There was no code.

    Tankado used to work at NSA. He was considered one of the best programmers at the NSA. He was fired from the NSA. He knew Strathmore's curiosity would get the best of him. He also knew of the filters built-in to TRANSLTR. Tankado tricked Strathmore into bypassing the filters (remember the mutation strings - he emailed himself to say that mutation strings were the key to success).

    Strathmore had to know for himself that TRANSLTR could not break the "code" so he bypassed the filters enabling the "worm" to wreak havoc with TRANSLTR. Because TRANSLTR wasn't really "stumped" cracking the code, and the security guard shorted the electrical system, the auxilliary power wasn't sufficient to power the freon cooling system, TRANSLTR overheated allowing the worm to infect the NSA database.

    The pass key wasn't the decryption for a code, there was no code. The pass key was an abort for the worm.

    The mutation strings were the key alright...the key to Tankado opening the NSA database to everyone in the world exposing that they were snooping. This is the main point of the story, not the mathematical accuracy of encryption/decryption schemes.

    Contributed by Emile

    On page 29 of my copy, the book had totally destroyed my ability to suspend disbelief. It says the NSA machine can check 30 million keys per second, that it's been working on this code for 15h:09m:33s and that therefore the key would have to be "over ten billion digits long."

    306 keys per sec works out to: (30*106)*60*60*16 = 1728000000000 keys in 16 hours

    264 = 18446744073709551616.

    So even giving Mr. Brown the benefit of the doubt, and assuming he is confusing digits and bits here as he does elsewhere, this machine couldn't even brute force a single 64 bit key in 16 hours, let alone a billion bit key. I don't expect perfect math or science from my fiction, but if it's technical fiction I'd at least like the basic premise to be within the realm of sensibility.

    I gave the mathematical content rating a 3 because it is definitly a main theme, but almost all the math actually in the book is wrong!

    Obviously, if everything else about the book was great and the author just happened to be math challenged it would rate better than a 1 in quality. But it reads like a romance novel! I don't understand what it is that people love in this book. Nor do I understand why it has not yet been made into a major motion picture; the studios wouldn't even have to dumb it down.

    Contributed by Owen

    I consider myself to be quite knowledgeable on cryptography, and I have never heard of anything called Bergofsky's Principle. OK, maybe I just never heard of it and it exists, but if it does, it's wrong. If Dan Brown had done even a little research, he would have discovered the one-time pad, a cipher that cannot be broken simply because given a ciphertext, any plaintext of the same length is a possible decryption of it.

    I know that NSA is capable of building an uber-brute-force machine (they probably already have a DES one), but I think the speed claimed by Brown is unrealistic, even for the NSA. Also, as other readers have pointed out, all the math of that (TRANSLTR's speed vs. the time it takes to decrypt things) is wrong. And of course the idea that it could brute-force a key without knowing the algorithm is completely ridiculous. Not even the NSA can get around not knowing the algorithm a ciphertext is encrypted with. You've got to have an algorithm to try brute-forced keys in.

    Also, the cipher used for the final puzzle (the prime difference one) and for the page-number puzzle is not called the Caesar Square. It's just a column transposition cipher.

    A couple of factual errors regarding public key crypto: the first one is just a little nitpick. Brown says that to decrypt a message encrypted under a PKC algorithm, you need to enter the sender's pass-key. You need to enter YOUR pass-key, the partner of the key the sender encrypted the message with...duh, obvious mistake. Another, more important factual error is that PKC was not invented by entrepreneurial programmers seeking a way to keep email more secure. It was invented in secret by the British equivalent of NSA, then independently reinvented by the now-famous RSA - Rivest, Shamir and Adleman. Or, if you prefer, it was reinvented by Diffie, Hellman and Merkle.

    However, I think that Digital Fortress did an excellent job of representing both sides of the battle over digital privacy. On the one hand, you've got NSA saying that they only use their near-limitless powers to protect national security, and that they need unrestricted access in order to fulfill their duty. On the other hand, you've got EFF and other civil rights groups claiming that everyone has the right to privacy and if that means unbreakable (even by the NSA) encryption, so be it. Before reading Digital Fortress, I couldn't choose a side. After reading it, I still can't choose a side. At least Brown wasn't blatantly biased (although I detected a hint of pro-NSA bias).

    Contributed by Bruce Bailey

    I feel fortunate that I didn't read Digital Fortress until after you reformatted this thread! I went looking for others opinions after I finished. I am out of the habit of reading science fiction, so this was my first leisure book in quite some time. I picked it up because of the math potential and Dan Brown's recent reputation

    I found it to be an entertaining read, but I gather from other's comments that this is partly because this was my first Dan Brown book. The thing that irritated me the most early on (Tankado not finding a partner who was equally moral) was nicely resolved, so I am glad I stuck with the book. I agree with others that the end was climax was needless drawn out.

    The early chapters hinted at more math, and I was quite disappointed with this aspect. At the very least I expected a gibberish pseudoscientific explanation of how TRANSLTR did its magic. I was disappointed that Dan Brown invented SkipJack rather than making references to a "secret background" to the very real Clipper Chip. These too things made my "willful suspension of disbelief" very difficult. [Note: See anonymous reply below. -ak]

    I was also certain that the code being inscribed on a ring would utilize topology. Surely, would not the key to "cyclic cleartext" depend upon a phrase with no clear beginning and end? This was certainly an opportunity lost, although I had no idea how Dan Brown would resolve the problem!

    Contributed by Anonymous

    Bruce Bailey's assertion that Dan Brown made up Skipjack rather than referring to the "real" Clipper chip is incorrect. Skipjack is the name of the cryptographic algorithm that was designed to be used in the Clipper chip. The details of the Skipjack algorithm are secret, though not because revealing the algorithm would compromise its encryption. The reason that it is secret is that revealing the algorithm would allow implementation without the key-escrow functionality which would allow law enforcement a back-door.

    [Click here for a] reprint of a report reviewing the Skipjack algorithm.

    Contributed by Sean

    I agree with most that the mathematics, cryptography, and internet/communications themes felt poorly researched and bordered at times on ludicrous. The first ten chapters were particularly painful, making the book difficult to start and the suspension of disbelief even harder. As with all of Dan Brown's books, however, it was one heck of a page-turner.

    To those who, like me, were disastisfied with the math and technology: a word of caution. While confusing bits and characters is a foolish mistake easily remedied by a bit of research, readers should bear in mind the publication date before posting. One of your commentors, for example, suggested Brown should have researched the NSA website. I can't find a record of one prior to March 2000, besides which do we really think the information there today existed in the mid 90's when Brown likely researched the book?

    Contributed by Tom C.

    The question that kept running through my mind as soon as it was mentioned (and if you think about it turned out to be key) is what practical value is "rotating clear code"? If it keeps changing it has no "clear meaning". Also if it were encrypted so well why did "The Gauntlet" recognize it right away as mutation strings? One more question: Do the numbers on in light print on the title page of the book have any significance or are they simply decorative or a decoy? Things that make you go Hmmmmm...

    Contributed by Andrew

    I have seen many peoples comments on the "unbreakable code". There is actually a very old method for doing this that is impossible to solve... use a book. Take a random book and use numbers to represent pages, paragraphs and word number, or simply word number. This is a method that was brought up in my high school algebra class, I was told that there are many encrypted messages that stand to this day. The advantage is that you need even more that the book, you need to know the edition as well. The words that are repeated can be taken from different pages meaning that repetition of words doesn't help decode it. Simple, easy way to encode a message and impossible to decode without the book.

    Yes, this is true. Essentially, it is the same as the statement that you need a "one time pad". Though, today's codes have a marvelous feature that these lack. Using the number theoretic "public key encryption algorithms", the person sending the coded message and the person receiving it do not have to have ever communicated before! Think about it this way: you go to and want to buy a book on their secure server. That is, you want to send your credit card information to them in an encrypted format. How could you do that using a code like the one you describe? There is no way...because first you and they would have to agree on the book to use and you would have to do that in a way that other people would be able to intercept and read. It is this important feature of these so-called "trap-door codes" that results in their wide-spread use today, even though they are theoretically breakable.

    Contributed by kjelt

    Hi there,

    I've just finished Digital Fortress (or "Diabolus" in the German translation)...nice book, a page turner, but not as good as "Angels&Deamons" or "The Da Vinci Code" by Dan Brown.

    There is two things that bothered me though, so maybe some of you know the answer:

    Why does the TRANSLTR pass whatever its cracking its teeth on (and I do agree with many critics here, that there are some hard-to-imagine facts about this piece of data in the book) to the databases? Was not TRANSLTR supposed to store such things AFTER it was finished decoding it? But it never does, because it kills itself before...

    Where do those comments come from? Didn't we read, that the bit from the internet was not decyphered? And still there are 64 characters found obviously in a SOURCE?

    May be some of you have some comments on that...

    Cheerio, kjelt

    PS: Alex, nice site!

    Contributed by René Dawir

    After finishing the book I read with great interest all the contributions on your website.

    I have a question about an unfinished phrase in the book:

    (quoted from Digital Fortress)

    Chapter 125: Soshi: "Primes are essential to Japanese culture! Haiku uses primes. Three lines and syllable counts of five, seven five. All primes. The temples of Kyoto all have ---"

    Do you know what all the temples of Kyoto have in relationship with prime numbers ?

    By a complete coincidence, one of my co-authors is a mathematician at Kyoto University. You would think that if there was some reasonable completion to this sentence, then he would know about it. However, it sounds as if he thinks it is bogus:

    Contributed by Taka

    I have some guess, although I'm not quite sure. It might be a five story pagoda. The tall, photogenic pagodas often make their way to touristic pictures. Not every temple in Kyoto, not even among the very big ones, has a pagoda. But those touristic photos might give false impressions to those who grew up in the west and have never been to Kyoto (except perhaps a short touristic visit).

    Indeed, the author might not be very familiar with Japanese culture. E.g., he said Haiku is written in 3 lines, but in Japanese it is much more common to write a Haiku in 1 line.

    Contributed by Rene

    Thank you for mail and your help!

    In the meantime I have made some searches, and found a website about Japanese garden. It said that in the Zen garden of the Ryoan-ji temple in Kyoto, stone groups are arranged following the "7-5-3 proportions of Shichigosan" (which is an archaic number range with old Chinese origins). What I don't know, if this is applicable to every temple of Kyoto.

    I then made a search about Shichigosan in relationship with Japanese temples and shrines, and found the following on Wikipedia: "Shichigosan (literally "seven-five-three") is a traditional festival day in Japan for children aged three, five and seven. It is on the fifteenth of November. Children who are aged three, five and seven will go to a shrine to drive out evil spirits. Old Japanese thought that on the age of odd number years, which is up to thirteen, something important would happen to the child. Today, boys who are aged three and five, girls who are aged three and seven will dress up in kimonos and have fun. They will eat chitoseame, which is a kind of candy, and wish to have a long happy life."

    Contributed by Taka

    I didn't know of the 7-5-3 proportions in the stone garden of Ryoanji, and I know nothing about the compositions in Japanese gardens, but any such rules you see there may be of technical or artistic nature rather than of religious or philosophical nature. I mean, such rules may have very likely been to make it easy for the gardeners (or architects) to design and create the garden. In the visual art and music, artists often follow rules or theories. Without rules, it's hard for artists to create and for people to appreciate. For instance, Schoenberg's works from his "really atonal" period (after he left the old world of tonal music and before he established the Dodecaphonie or twelve tone music) were made without rules, if I understand it correctly. They must have been hard for him to compose, and they turned out to be hard for us to appreciate.

    And even if there is something real in the garden's 7-5-3 proportion, it's hard for me to believe that there is any relation of it to our tradition of celebrating kids of ages 7, 5 and 3 in November. First, in this shichi(7)-go(5)-san(3) event, we bring kids to shinto shrines, rather than buddhist temples. Second, stone gardens are only in those minimalistic zen temples and thus give me an impression that they are very special. (In most of Japanese gardens in temples, you see trees and water (waterfalls, ponds, etc) besides pieces of rock.) Zen buddhism belongs to samurai culture. On the other hand, I may be wrong but my impression is that the shichi-go-san event seems to be a people's tradition. They differ as much as noble, court music and profane, folk music. I don't mean the latter is lower (I don't really -- as a big fan of Bartok, I believe folk music can have very high artistic values and can be real treasure of human history), but they are different.

    I may be really wrong. Born and grown up in Japan doesn't mean I have any authority to answer his question. It's just what I think. Just my two cents and no more. --taka

  • What non-mathematical errors are in the book?

    Many readers complained about non-mathematical errors, some logical and some that just reflected an ignorance of a particular city which appears in the book. In the case of most authors, such little mistakes are not so bothersome. However, since Brown likes to pepper his books with facts as a way of making them seem almost educational, it is frustrating that so many of them turn out to be wrong. Here are just a few:

    Contributed by Dan Marlow

    I just finished Digital Fortress  and found it somewhat entertaining.  However, at the end, when the author goes to such extremes to have the key found, why the business about "a common misconception" that the second bomb dropped on Japan used U-239.  Mr. Brown then goes on to state that U-238 was used.  Every authoritative book I have ever read states without qualification the U-239 was the material used in the second bomb, as well as the very first bomb exploded in New Mexico.

    Contributed by Mike Najera

    I have read several web pages and some books about the atomic weapons and the second bomb (Fat Man), according to all the sources, used Plutonium, not Uranium. three sources: both of which state Plutonium was used as the fuel in Fat Man, but the last source states that the Plutonium was surrounded by a sphere of Uranium 235. I think what is in the core is considered the fuel.

    Contributed by Anonymous

    revolvers can not be silenced, only automatic pistols can be silenced.

    (Prompted by an e-mail message from Will Mann, I looked around a bit on the internet and found that the previous comment is an overstatement. Most revolvers cannot be silenced, but there are a few rare revolver models which can support a silencer.)

    Contributed by Bob S.

    ...and the NSA being described as being "hidden discreetly" in the wooded hills of Ft. Meade. YOU CAN SEE IT FROM THE BALTIMORE-WASHINGTON PARKWAY! And the National Cryptologic Museum is run by the NSA and is located between the parkway and the NSA complex.

    Contributed by Anonymous

    I don't have the knowledge to really comment on the math portion, but pretty much every scene featuring the NSA made me cringe. I work in the US intelligence community, and while I haven't yet worked at NSA, many coworkers have. Security in the book is amazingly lax, and in real life nobody would have been able to have mobile phones in the building. If you are caught with one, it is taken from you, the internal memory is scrubbed, and it is totally dismantled to be checked for bugs before it is returned to you, along with a letter of reprimand, and if you are military, possibly loss of rank. In addition, DIRNSA, the director of NSA, is always a 3-star general or admiral, never a civilian. There is much more that irritated me, but it's been over a year since I read it, and I don't remember much else.

    Contributed by Leroy Meyers

    Hi. I just finished Digital Fortress, and I came across 3 non-math problems. If you have an explanation, please let me know ( 1. Why would the authorities in Seville say that Tankado dies of a heart attack (natural causes)? I would think that someone would have to examine the body to determine the cause of death, and would have seen the mark on his chest from the projectile that Hulohot shot. The lieutenant in the morgue said he was told it was a heart attack. 2. Strathmore's plan was to build a back door into Digital Fortress and make an internet switch. But in Chapter 7, it says that every software company in Japan has downloaded an encrypted copy already. Why would Strathmore think that a company would download the new version with the back door when they already have a copy? 3. After David's encounter with the call girl and German man, it's a good thing he stopped for a drink, or else Hulohot would not have had time to assault a maid, kill 2 people, and still stay on David's trail!

    Contributed by pino

    If there was Freon pouring down over the core of TRANSLTR, A) they would have needed about a million tons of the stuff, and B) it is primarily a liguid at 90degcC below freezing, and C) in the fire they would have all died within 10 minutes as when freon burns it forms phosgene [which is poisonous, but not the same as mustard gas as Pino originally claimed here -ak.]! Mr Brown should have researched this a bit better and asked a fridge engineer for advice, but then in a country that shuns Kyoto, what would he care?

    Contributed by Tuppy

    Dan Brown's books are no exception. Here are just a few of my observations:

    The 'Hero' David while admitting to hate motorcycles has the necessary skills to ride a Vespa 'motorcycle' (I think he means scooter) at top speed across an oil slicked hanger, grass, kerbs, a highway divider and cobbles, while being chased and shot at without falling off. Total lack of security at Seville airport allowing a bike and car on to the runway.

    The Vespa 250 (200 more like) with a fuel gauge and fuel tap under the tank?

    Several cheap jibes at Spain: medieval Spanish medical facilities and practices. Not knowing the difference between the various Spanish Police forces and getting totally confused between the Guardia Civil and Seville.

    The Nazi Enigma machine a 12 ton monster? Must be dark matter in that typewriter sized wooden box.

    A room 121 feet underground that need 280 tonnes of earth to be excavated. A cubic metre of soil weighs about 1 tonne. How small is the database computer room? 21 feet long, wide and high? You do the maths, but I recon 280 THOUSAND tonnes would not be far out, that gives you a hole 30 metres square and deep.

    So, based on my observations, I can only surmise that the bits I don't know much about are all to the same the same standard of the Isle of Wight Ferry* as the bits I do know about.

    Conclusion: Badly researched techno fiction with cheap Mills and Boon sub plot. It could be so much better. Brown and his editor should be ashamed to produce such weak material.

    *It's brown and comes out of Cowes backwards.

    Contributed by Megan

    Although I did enjoy the novel, I was rather disappointed with the climax where a person who is a mathematician for a living and has an IQ of 170 failed to solve the code for the kill code of the worm. In particular, not realising the inflections of the words "prime" and "difference" in this mathematical context. I may only be taking Maths at A-level and have an IQ of 130, but I managed to solve the problem a considerable while before the "brilliant and beautiful mathematician" Susan Fletcher!

    Contributed by Philipp Spitta

    After reading the book, which I found amazing, I had a look at the NSAs website. And found out, that only American citizens could become an employee. So how did the Japanese guy get into the organization?

    Contributed by Donn

    I cannot add anything to the mathmatical discussions here or the code discussions. I agree pretty much with the majority. I would like to say that revolvers generally do not work well with suppressors (what hollywood calls 'silencers') because of the gap, however small, between the cylinder and the barrel. That gap will always release some gas from the round being fired and with that, some noise. Semi-auto handguns are a completely different design and do not have such a gap. I was wondering, though, why the main data banks of the NSA don't have any kind of anti-virus program. Surely, there is data entering the system from other points than TRANSLTR? Oh, why is the machine called TRANSLTR? Is it an acronym for something? Or did they just spell 'translator' wrong? That could explain why nobody noticed NDAKOTA was Tankado? Or why, when presented with the fact that Tankado was simply e-mailing himself, Strathmore didn't believe it? One last thing. Who designed the physical machine of TRANSLTR? Since they knew it was a flammable design that had to be kept cool with freon, why didn't they build any sort of fail-safe auto shut down sequence if it got too hot? OK, rant over...

    Contributed by Dave Barber

    Having read all of the other 3 Dan Brown novels and generally enjoying them (albeit invariably ripping them to shreds on consistency and ultimately having close on identical plots), this was the first one that I couldn't complete.

    Its quite a while (several years) since I read it, so the details may be fuzzy. My area of expertise is database design, and I spent several years at a major UK military site that was (probably) under similar security to the alleged NSA offices.

    One of the protagonists got a password via a physical key logger - bits and pieces were brought in and a keyboard modified? I don't buy it at all. The physical security of these sites is beyond the electronic security (ie. total paranoia at all levels), and the chances of somehow being able to modify a keyboard is more than just unlikely, it strikes me as being impossible.

    Maybe US military security isn't quite as tight as that in the UK .... ?

  • Who is Dan Brown's father?

    Brown, whose Website contains lots of information about his books (and lots of pictures of himself) is the son of a "Presidential award winning math professor and a professional sacred musician". (Anyone know exactly who his father is?)

    Contributed by Anonymous

    I was also intrigued by the identity of Dan Brown's father, thinking that he could be one of several famous mathematicians with last name Brown. In one of his books he refers to his father as Dick, whence I looked in the AMS (=American Math Society) database (MathSciNet) for any Richard or Dick Browns but none seemed obviously of "Presidential Award" calibre. I then realised that in the US "Mathematics Professor" could refer not to a mathematician but to a teacher of mathematics. I then googled "Presidential Award" and came across There is a Mr. Richard G. Brown teaching maths at Exeter who was awarded a Presidential Award in 1989. I'm willing to bet this is him.

    Thank you for your detective work, anonymous British contributor!

    Contributed by Shauna Hedgepeth

    First, I love your site - I just found it about 45 minutes ago and I can't seem to get away from it. I teach advanced math and I coach the MathCounts team at my middle school. I have been looking for books/movies to show my teenage students and your list has been a very helpful tool in making my list for next year. I had the honor of attending a lecture by Dan Brown's father, Richard, at the NCTM Regional Conference in New Orleans last year. He is now retired from teaching but lectures at conferences from time to time. His enthusiasm for mathematics (and the presence of the Fibonacci sequence in nature) was inspiring. I asked what Dan Brown book was his favorite and he said he loves "Angels and Demons". I only wish Dr. Brown WAS still teaching. If his courses are anything like his lecture, I would sign up immediately.

  • What is the solution to the code?

    Contributed by Becky

    I would like to know the solution of the code at the end of Digital Fortress.  Can you help?


Contributed by Gino Tramontelli

The code is not as complicated as you might think.  Take another look.  ***Here's the way you decode it*** Take the numbers and arrange them in 4 vertical columns of 4 numbers.  It should look like this:  
10 12861
85112126 78

Each number corresponds to a chapter in the book, in which the first letter is conveniently larger than the rest.  That is the letter that each number stands for. Using that method, you end up with:  


"We are watching you."

  Perhaps Dan Brown intended for multiple decodings, but I can't see how any could be more clear than that one.

Contributed by Srushti

Just finished reading Digital Fortress two hours ago and have been trying to crack the code since then. I finally had to give up and came searching for answers on the net.

Gino's explanation makes a lot of sense but I'm as stumped as Lorlie ...... do tell, does the hardcover follow a special font system? Because I have a St.Martin paperback and every chapter beginning follows a consitent Font size and style. If that is so, then I can heave a sigh of relief and reassure myself that I'm not a dunce coz I was reeeeallllly dissapointed when I couldnt solve this code. Ceasar's Box was an obvious part of the solution and I've tried every single alphabet-numerical substitution I could find !!!

Contributed by Brett Shingledecker

Re: the puzzle solution at the end, indeed it is a caesaring box and the chapter numbers corrspond to the letters, thus WE ARE WATCHING YOU. However, the previous layout in this website for the caesarian box is incorrect. if you list the numbers sequentially from top left going down the left column, moving from top to bottom, left to right (columns) insread of left to right (rows), then you get the solution spelled exactly right. The previous solution leaves one to believe that it is an anagram once solved. It actually spells out WE ARE WATCHING YOU if you read down the first column, then down the second, etc...

Contributed by Hessel

I've read a Dutch translation of the Digital Fortress (called "Het Juvenalis Dilemma"). The code mentioned at the end is a translated version as well and spells, using the Cesarian square & chapter numbers method, "Er wordt op je gelet". This means "You are being watched". So I think this is the final proof that "We are watching you" is the correct answer, since the meaning is (almost) the same as "You are being watched".

Contributed by Eyal Peleg

I saw you web page about this and I have some ifno you can add: In the hebrew translation of the book the code is a different one: it is 52-15-121-2-33-2-39-33-39-100-15-33-76-107-48-8 and has a small arrow below it indicating a right to left direction of reading. They used basicly the same method for the code, 16 numbers representing the first 16 letters of the coresponding chapters, only that the letters are not larger in thair fonts. The sentence created after setting the letters in a 4x4 squere from right to left and top to bottom (being hebrew) and reading from top to bottom and from right to left is the hebrew translation of what was written on tankado's ring "Quis custodiet ipsos custodies" which in hebrew transcript is "MI YISHMOR AL HASHOMRIM" - who will watch the watchers

Contributed by devil40tr

My comment is the solution to the final key... The correspondance to the chapter is quite ok...But the matrix is put the wrong way.. If you count the number of the characters it is 16 which is a "Perfect Square" and using the "Ceasar's Logic" the matrix should have read ;

w e c g
e w h y
a a i o
r t n u
and you have to read the sentences top to
we are watching you...

Contributed by Mead

i am 14 and have just finnished deception point which is another of dan brown's books, like digital fortress at the end it has a series of at first glance random numbers, but if u put it into a ceasar's box cipher and take the first letter from the chapters listed and read top to bottom you get the message "the da vinci code will surface"

Contributed by Rob Herod

Hi Alex I have just come across your website - it's great! I have been reading the entries about Dan Brown's Digital Fortress - very interesting. A bit of trivia - someone else might well have spotted this but here goes... My copy of Digital Fortress is a paperback edition published by Corgi in Great Britain 2004 so this might be their fault ... In this edition towards the end, in Chapter 120, when 'they' realise Tankado has left clues in his program code the following characters are listed:


which David realises can be written as a Caesar Cipher/Square or 'Box' as the text states. If you do this you actually get the message: Prime difference between elements resMonsible for Hiroshima and Nagasaki!!! At the start of Chapter 121 where the Caesar Square is shown the 'M'has changed into a 'P' so making the correct message: Prime difference between elements resPonsible for Hiroshima and Nagasaki

I also thought that the fact that N. Dakota is an anagram of Tankado would have 'jumped out' at one of the world's greatest cryptogtaphers but hey, the story would then have been over too soon and we can't have that!

All said, I thoroughly enjoyed reading Digital Fortress as I have enjoyed all Dan Brown's other books - there might well be errors in them but they sure are, in my opinion, great reads.

Contributed by Anonymous

I have a St Martin's paperback version and the same mistake is made there -- "M" instead of "P" in both strings in Chapter 120. So it doesn't appear to be the publisher's fault. Would Dan Brown have made this mistake in his original manuscript and no one ever caught it? Seems surprising.

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