Upping the password ante

 kw: computer security, passwords, analysis

Almost thirteen years ago I wrote about making "million-year passwords", based on the fastest brute-force cracking hardware of the time, that was approaching speeds of 100 billion hashes per second. The current speed record I can find is only 3-4 times that fast, at just over 1/3 of a trillion hashes per second, but it is a lot cheaper. It seems the hardware scene hasn't changed as much as I might have thought.

I surmise that more sophisticated phishing and other social engineering schemes have proven more effective than brute-force pwd file crunching. However, the racks of NVidia GPU's being built to run AI training are ramping up the power of available hardware, so I decided to make a fresh analysis with two goals in mind: firstly, based on a trillion-hash-per-second (THPS) potential rate, what is needed for a million-year threshold?, and secondly, is it possible to be "quantum ready", to push the threshold into the trillion-year range?

I plan to renew my list of personal-standard passwords. The current list is five years old, and contains roughly twenty items for various uses. I have more than 230 online accounts of many types, so I re-use each password 10-15 times, and I activate two-factor authentication wherever it is offered. The current "stable" of passwords range from 12 to 15 characters long. I analyzed them based on an "All-ASCII" criterion, but since then I've realized that there are between six and 24 special characters that aren't allowed in passwords, depending on the standards of various websites.

The following analysis evaluates six character sets:

1. Num, digits 0-9 only. The most boneheaded kind of password; one must use 20 digits to have a password that can survive more than a year of brute-force attack.
2. Alpha1, single-case letters only (26 letters).
3. Alpha2, both upper-and lower-case letters (52)
4. AlphaNum, the typical Alphanumeric set of 62 characters.
5. AN71, AlphaNum plus these nine: ! @ # $ * % ^ & +
6. AN89, AlphaNum plus these 27: ! @ # $ % ^ & * ( ) _ - + { } [ ] | \ : ; " ' , . ? ~

The only sets that make sense are AlphaNum and AN71. The shorter sets aren't usually allowed because most websites require at least one digit, and usually, a special character also. AN89 provides a few extra characters if you like, but almost nobody allows a password to contain a period, comma, or any of the braces, brackets and parentheses. I typically stick to AN71.

The calculation is straightforward: take the size of the character set to the power of the password length. Thus, AlphaNum (62 in the set) to the 10th power (for a 10-character password) yields 8.39E+17. The "E" means ten-to-the-power-of, so 1E+06 is one million., a one followed by six zeroes. Negative exponents (the +17 above is an exponent) mean the first digit is that many characters to the right of the decimal point.

Next, divide the result by one trillion to get seconds; in scientific notation, just subtract twelve from the exponent, which yields 8.39E+05, or 839,000 seconds. The number of seconds in one year is 86,400 × 365.2425 (86,400 seconds per day, 365.2425 days per Gregorian year). Divide by this; in this case, the result is 0.0266, or about 9.7 hours.

Are you using a 10-character alphanumeric password? It will "last" no more than 9.7 hours against a brute-force attack with a THPS machine. If you were to replace just one character with a punctuation mark, such as %, the machine would find out, after 9.7 hours, that your password is not alphanumeric with a length of ten. It would have to go to the next step in its protocol and keep going. If its protocol is to run all 10-character passwords in AN71 (perhaps excepting totally alphanumeric ones, since they've all been checked), 71 to the tenth power is 3.26E+18. The number of seconds taken to crack it is now 3.26 million, about a tenth of a year: 38 days.

We're still kind of a long way from a million-year level of resistance. To save words, I'll present the full analysis I did in this chart.

The chart is dense, and the text is rather small. You can click on it to see a larger version. The top section shows the number of seconds of resistance each item presents, with one hour or more (3,600 seconds) highlighted in orange. The middle section lists the number of days, with a pink highlight for more than seven days. The lower section lists the number of years with four highlights:

• Yellow for more than two years.
• Blue for more than 1,000 years.
• Green for more than one million years.
• Pale green for more than one trillion years, what I call "quantum-ready".

For what I call "casual shopping", such as Amazon and other online retailers, the "blue edge" ought to be good for the next few years. For banking and other high-security websites, I'll prefer the darker green section. That means, using AN71, I need 13-character passwords for the thousand-year level, and 14-character passwords for the million-year level.

There is one more wrinkle to consider: The numbers shown are the time it takes a THPS machine to exhaust the possibilities at that level. If your password is "in" a certain level, it might not last that long, but it will last at least as long as the level to its left. For example, AN71 of length 12 shows 520 years. Not bad. If you have an AN71 password of length 13, the cracking machine would need 520 years, to determine it isn't 12 characters or fewer, but once it starts on 13-character passwords, maybe it will take it half or more of the 36,920 years indicated to find it, but it might luck out and get there much sooner. But it still consumed 520 years getting this far. Anyway, if you're going for a certain criterion, adding a character makes it definite that at least that length of time would be needed for the hardware to get into the region in which your password resides.

Another way to boost the resistance is to have at least two special characters, one (or more) from the AN71 set, and at least one from the rest of the AN89 set, such as "-" or "~", wherever a website allows it. Then a machine that checks only within AN71 will never find it.

With all this in mind, I plan to devise a set of passwords with lengths from 13 to 16 characters, using primarily AN71. On the rare occasion where I can't use special characters, I'll have AlphaNum alternatives with 14 to 17 characters prepared. I'll test if I can use a tilde or hyphen, and use one of them if possible for the really high-security sites.

A final word about password composition. I actually use pass phrases with non-alpha characters inserted between words or substituted for certain letters, and occasional misspellings. Starting with a favorite phrase from Shakespeare, Portia's opening clause, "The quality of mercy is not strained", one could pluck out "quality of mercy" (16 characters) and derive variations such as:

• qUal!ty#of#3ercY
• QW4lity70f8M&rcy
• quality$of~MERC7
• qua1ity2of2M3rcyy (AlphaNum with an appended letter)

…and I could add more than one character in place of the space(s) between words…

It is also worth keeping abreast of news about quantum computing. What exists today is dramatically over-hyped. It may not always be so. But I suspect a trillion-year-resistant password will remain secure for at least a generation.