Previously, I used entropy as a backdrop for creating strong passwords. It's important that you read that article and fully understand it before moving on with the rest of the series.
Now let's begin generating passwords. We'll start off first with Diceware.
Diceware
Diceware meets these 2 qualifications that we should use when building our passwords. However, Diceware prefers to call them "passphrases", rather than passwords, as your password will actually be multiple words stringed together, rather than just a single word. The passphrase is built by rolling 5 fair 6-sided dice (or 1 fair 6-sided die rolled 5 times), and looking up the results in a word list.
The word list comprises of 7,776 words (the total number of combinations from 5 fair 6-sided dice). Each word has a look up number that corresponds to the dice roll. For example, if you rolled "44311", then your first word from the word list would be "oint". I say "first word", because you now need to make another roll. You need to continue rolling until your passphrase contains at least 80-bits of entropy.
Because there are 7,776 possible words in the word list, then each word contains about 12.95 bits of entropy. This means you will need to roll your 5 dice seven times (six rolls will only produce 77.7-bits of entropy) to achieve the minimum. Starting with my first word, and rolling six more times, here are the results of my dice rolls:
44311 oint 12115 alum 16335 cg 64566 xs 22213 cut 43221 mutt 53143 scar
Or, "ointalumcgxscutmuttscar", which is 23 total characters in length. This is a semi-lengthy password, no doubt, but it meets our criteria to be truly random and contains sufficient entropy. Further, because the word list can be printed, you can generate secure, and strong passwords without the aid of a computer.
Variation 1- Portable Diceware
Carrying around a word list of 7,776 words might not be very practical. After all, if you store it in your wallet, assuming you can hold something about 10-by-30 characters on each side of a card, you would need to print close to 175 cards to fit all the Diceware word list. This just isn't practical. You could store the word list as a PDF, and carry it on your phone, but not everyone has a phone capable of installing a PDF reader, and we're trying to achieve this without the aid of any computing device. Let's dig further.
For carrying around only one or two cards in your wallet, we'll need to generate some tables. Thankfully the tables are small, and you can still generate secure passwords. Unfortunately, the passwords will not be as easy to remember as using the original word list. Consider the following table:
If first roll=1 or 2 3 or 4 5 or 6
Second Roll Second Roll Second Roll
1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
T 1 A B C D E F a b c d e f ! @ # $ % ^
h 2 G H I J K L g h i j k l & * ( ) - =
i 3 M N O P Q R m n o p q r + [ ] { } \
r 4 S T U V W X s t u v w x | ` ; : ' "
d 5 Y Z 0 1 2 3 y z ~ _ sp < > / ? . ,
6 4 5 6 7 8 9
In this case, I will only need 3 fair 6-sided dice (or 1 fair 6-sided die rolled three times), rather than 5. Suppose I roll "614". The "6" means I would use the third table. The "1" means the first column in the third table, and the "4" is the fourth row in the 1st column of the third table, or "|". All 94 printable ASCII characters, plus the space, are represented in these tables. Each character gives about 6.57-bits of entropy, which means you would only need to roll your 3 fair 6-sided dice thirteen times to get enough entropy to meet our requirement for at least 80-bits of entropy.
As an example, consider the following rolls:
614 622 224 461 424 155 565 113 255 322 136 631 544
This would produce:
614 | 622 * 224 T 461 f 424 t 155 2 565 , 113 M 255 2 322 h 136 6 631 # 544 :
Or "|*Tft2,M2h6#:" as our password. This password contains 85.41-bits of entropy, and was created at random. The characters "sp" represent the ASCII space. If you reach a table blank on any of your rolls, such as rolling "616", or "365", just roll again.
If you only need to create a password that uses just letters and numbers, then you only need to use the first table, and you only need two dice. However, each character only gives about 5.17-bits of entropy. As such, we would need a 16-character password to achieve our 80-bits minimum.
There are other variations on the tables with dice that you can use, such as generating random hexadecimal strings, random decimal numbers, special characters, and other requirements. See the Diceware FAQ for more information.
Variation 2- Dictionaryware
While carrying around a word list in your wallet or purse might not be practical, you may have a dictionary in your bookshelf, or the place you are visiting might have a dictionary you can borrow. The tricky part about dictionaries, however, is determining your search space, so you can accurately calculate entropy. Thankfully, we just need to put on our thinking caps, do a bit of math, and we can arrive at a good number.
My Merriam-Webster Dictionary contains approximately 57,000 defined words, across 820 pages of printed text. This averages to 70 dictionary words page. Each page is divided into two columns, which gives me about 35 dictionary words per column. I'll use the same 5 fair 6-sided dice I used in my initial Diceware. Because my dictionary book contains 3 numbers for its page number, the first 3 dice will tell me the page number of the dictionary. The 4th die will tell me which column the word will come from; if the die is odd (1, 3, or 5), the first (left) column is used, if the die is even (2, 4, or 6), then the second (right) column is used. The 5th die will tell me the word in that column, which means only using the first 6 words in each column.
As an example, if my roll was "56351", then I would turn to page "563", use the first column on the page, and the first word, which is "Pullman".
Obviously, there are a great number of pages skipped, and a lot of words skipped. To understand how much entropy each word provides, I need to figure out how many words are available given my limitations with 6-sided dice. First, the following pages in my dictionary are skipped:
- 1-110 (a-calm)
- 167-210 (convolution-disgust)
- 267-310 (festoon-GQ)
- 367-410 (inhale-litigious)
- 467-510 (natty-patchwork)
- 567-610 (QM-rumble)
- 667-820 (stab-zymurgy)
That's a total of 484 pages eliminated from the book, which means I only have 336 valid pages to use. Because I can only choose the first 6 words from each column, or 12 words per page, that gives me 4,032 total words available to pick from. As such, each word provides about 11.98-bits of entropy, which means I need at least 7 words from my dictionary to reach my 80-bits entropy minimum for my passphrase.
As an example, if I use my rolls that I used at the beginning of this post, then my result would be:
44311 midday 12115 castled 16335 constancy 64566 skew 22213 drag 43221 maunder 53143 plantain
Or "middaycastledconstancyskewdragmaunderplantain". That's 45 characters in length, which is rather lengthy to achieve the minimum amount of entropy as our initial Diceware roll at the start of this post. This is due to the possibility of words in the English language being longer than 7 characters, which doesn't exist in our Diceware list. As such, you will likely get longer passphrases using an English dictionary versus using the Diceware list.
Some points to take into consideration when using "Dictionaryware":
Different dictionaries will need to be adjusted as necessary to accommodate the number of pages, and the number of columns. You just need to make sure that the dice are picking the word, and not you. If your dictionary is smaller than 600 pages, you may need to come up with a system handling the numbers 0, 7, 8, & 9 to get sufficient entropy. Additional dice rolls or a look up table could work, but it complicates the process.
Some dictionaries might define a word two, three, or times, based on it being a noun, verb, adjective or abbreviation. This will reduce our total search space, which will reduce our entropy per word. So, in my example of 11.98-bits of entropy per word, this is a maximum. It may require a bit more work to determine a more accurate entropy estimate.
Variation 3- Coinware
Even carrying around dice can be impractical. However, it is much more likely that you are carrying around spare change in your pockets, or have some sitting in a desk drawer at work. Provided that the coin flips fairly between heads and tails, you can flip a coin to build your passphrase.
Preferably, you'll want to use 3 separate coins (penny, nickel, dime), but if you only have a single penny, or 3 pennies, that will work too. The idea is that you toss the three coins, which will identify a single throw of a die. So, 15 coin tosses will determine your 5 dice rolls. Using Coinware requires the following look up table:
Results of Coin Toss
Penny Nickel Dime
D 1 T T T
i 2 T T H
e 3 T H T
4 T H H
R 5 H T T
o 6 H T H
l * H H T
l * H H H
If your coin tosses produce a "*", re-flip your coins. As such, to get the dice roll of "44311", I would have needed to get the following coin flips:
THH 4 THH 4 THT 3 TTT 1 TTT 1
This would produce my word "oint" from the Diceware word list. I would then need to proceed six more times to get my seven words necessary for reaching my 80-bits of entropy minimum. If you think that flipping 3 coins for 1 die roll is a lot of work, you're right. It is. You would be better off getting some dice.
Dice Considerations
I would be amiss if I didn't mention something about the randomness of dice itself. No doubt, dice can be loaded, imbalanced, burned, and/or lopsided to favor certain sides. For obvious reasons, you should avoid using "bad dice" when generating your Diceware passphrases. You want random to be on your side as much as possible (you want a "strong password", don't you?). Every side of each die should be equally as likely as the other five sides.
Unfortunately, "gaming dice" that you get from your local hobby store, or that come with board games, aren't fair 6-sided dice. But, they're probably "good enough". In other words, one die may favor a "4" due to imperfections in the die material, weighting it on the "3", while another die may favor a "6", because it has had more material drilled out of it than the "1". Finally, one die may have a more chamfered corner or edge than the rest of the corners or edges, slightly favoring a specific number or pair of numbers. Taking these imperfections, and the position the dice fall with respect to the others will probably give you enough randomness as to not be repeatable from throw-to-throw.
If you want to see if your dice favor numbers, get a tall cylinder, such as a large water bottle. Fill it with water, and drop in your die, then seal off the top. The die will sink to the bottom. Turn over the cylinder, let the die drop to the bottom, and record its number. You should do this at least 30 times for a decent sample size. In fact, the larger the sample size, the more accurate the results. Each number should come up 1/6 of the time, for that die. See Playing Fair with the Chi Square Test of Homogeneity for more information about testing fairness in dice.
However, there are "precision dice", or "casino quality dice" which are guaranteed to have each number equally as likely as the other six within a .0001 margin of error between any two numbers (in other words, if you threw the die 10,000 times, a favored number would come up 1 more time than another). If you live close to a casino, you can probably purchase used casino dice on the cheap. Even though the corners and edges will be slightly chamfered, thus beginning to show slight favoring in numbers, they are still likely more "fair" than your store-bought dice, and will probably continue to exhibit more fairness in each throw for a good long while.
If you search for "precision casino dice", you will find some listings on Amazon, eBay, and other locations. Most of these dice have razor edges and corners, meaning they are not rounded, and the corners are sharp. As such, the dice don't "roll" as well as dice purchased from a hobby store. They tend to land with a solid fall on the number. This also means they won't roll off your table when throwing them. Many of these dice will be transparent, so you can see the pip depth, and will also have a serial number printed on the die if purchased in a set. These dice are more expensive, but they will be the best choice in choosing fair 6-sided dice.
Rix Dice are precision machined metal dice, with chamfered corners and edges for better rolling. They'll last longer than acrylic or plastic dice, and the creator, Amber Rix, has paid attention to the dice being fair. They might be a consideration, if you plan on rolling them a lot. They are the most expensive precision dice I've come across, but probably the most durable too.
Conclusion
Diceware, and it's variants, can be a secure way for generating strong passwords that would withstand even the most sophisticated offline attacks on a hashed password database (which is the real threat). If you pay attention to entropy and randomization, then you'll create strong passwords that we qualified at the beginning of this post. As such, even the most powerful brute force searches on a hashed database, won't reveal your password. And Diceware makes it easy to remember your password, using only lowercase letters.
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