Passwords are easy to generate, easy to record.. but still nobody likes 45-character passwords!

I like to use diceware to generate legible, secure passwords. Generally, each word (out of 7,776) will add ~12~13 bits of entropy. This requires 5 six-sided dice to be rolled for each word.

6 words is plenty, good enough for just about anything. 4 words is enough for maybe your Netflix password1.


I’ll use hand-rolled examples to show how weird the words can be. Base64 sprinkled in liberally. Don’t use these passwords, obviously2.

Pattern bits of entropy
= 2·log2(65) + 3·8 49.85 bits
= 4·log2(65) 51.70 bits
= 3·log2(65) + 3·8 62.77 bits
= 5·log2(65) 64.62 bits
= 2·log2(65) + 6·8 73.85 bits
= 4·log2(65) + 3·8 75.70 bits
= 6·log2(65) 77.55 bits
= 3·log2(65) + 6·8 86.77 bits
= 3·log2(65) + 9·8 (base64)[^3] 110.77 bits

So a little base64 goes a long way. Too bad it’s hard to write down accurately, let alone remember.

Equivalent entropies

Some more common styles of passwords, for comparison (in increasing entropy):

Pattern equation bits of entropy
1234-56-7890 log2(10,000,000,000) 33.22 bits
wCEHMbIs 6·8 48 bits
abcdefghijklm 13·log2(26) 61.11 bits
H65j/aS5vfmm 9·8 72 bits
0mE07rdje4xzvxUE 12·8 96 bits
aT7bubJTM4w2RoyeNPsQ 15·8 120 bits

64 bits indeed seems “long”.

A lot of bad password policies (6 chars only, 8 chars only..) keep you around 30-40 bits.


I like MotocrossVarietyGaveScroll-jj+G (75.70 bits) for long passwords, and MotocrossVariety-jj+G (49.85 bits) for shorter ones. I like to be able to write them down more than I like them super short.

Generating these requires 2-4 dicerolls (& a diceware textfile lookup) and a quick openssl rand -base64 3.

64 bits is IMO “pretty good”. If you need 256 bits, you’re not really talking about a password any more, but a key. You can generate just lots more bits to come out of openssl, if that’s what you’re after

$ openssl rand -base64 32


I don’t use a lot of long passwords, but looking back: MotocrossVarietyGaveScroll-jj+G (75.70 bits) is just super long. 31 characters!? I wouldn’t even try to remember those.

Why not go straight base64 at that point? 21 bytes gets you 28 characters. 18 bytes gets you 24 characters. That’s 144-168 bits of entropy. Way beyond normal stuff. Here’s a better “long” password:

If you can use a 20-character password, use 15 random bytes (120 bits) :

  $  openssl rand -base64 15
aT7bubJTM4w2RoyeNPsQ     # results should vary..

This is way overkill, but a 20-character password is quite long and might as well be used.

You might need to add a special character (pick your favorite..) and maybe a number. I guess, technically, you might land all 1s or something crazy, so maybe append a Az1! or something to fulfill all those nice password requirements. You may have to trim some bits to make it fit, if 24 characters is too many.

  1. typing, on those little remotes, is like maximum annoying 

  2. but also don’t avoid them, if you truly do roll them.. riiiight?