2016-06-15: rigorously document the strength of secure passwords.

rigorously document the strength of secure passwords.

diff --git a/examples/securepassword.w b/examples/securepassword.w
--- a/examples/securepassword.w
+++ b/examples/securepassword.w
@@ -10,9 +10,22 @@ exec guile -L $(dirname $(dirname $(real
 ;; According to a recovery company which sells crackers at 1.5k$, as of
 ;; 2016 a zip-file can be attacked with 100,000 guesses per second.
 
+;; Codinghorror quotes[1] codohale[2] on the cost of buying 5 billion
+;; cracked md5 hashes per second in 2010 for just 3$ per hour. This
+;; should be around 20 billion guesses per second today.
+
+;; [1]: https://blog.codinghorror.com/speed-hashing/
+;; [2]: http://codahale.com/how-to-safely-store-a-password/ 
+
 ;; A password with 8 letters and 2 delimiters (length 8, entropy 50)
-;; would on average withstand the strong attack for 2.5 days, the weak
-;; until 2032 (when it would be cracked in one year), assuming
+;; would on average withstand the strong attack with a single device
+;; for 2.5 days. It would take around one day to crack with 20 billion
+;; guesses per second, so you could buy a cracked md5-secured 8 letter
+;; + 2 delimiter password for 72$ (assuming that it was salted,
+;; otherwise you can buy all these md5’ed passwords for around 144$).
+
+;; The 8 letter and 2 delimiter password would withstand the weak
+;; attack until 2032 (when it would be cracked in one year), assuming
 ;; doubling of processing power every two years. Cracking it in one
 ;; day would be possible in 2049.
 
@@ -24,7 +37,60 @@ exec guile -L $(dirname $(dirname $(real
 ;; For every factor of 1000 (i.e. 1024 computers), the time to get a
 ;; solution is reduced by 20 years.  Using every existing cell phone,
 ;; the 12 letter key would be cracked by the method with 100,000
-;; guesses per second in 2039. Facebook could do that with Javascript.
+;; guesses per second in 2039 (within one year). Facebook could do
+;; that with Javascript, so you might want to use a longer password if
+;; your data has to be secure for longer than 22 years.
+
+;; Using Landauer’s principle[3], we can estimate the minimum energy
+;; needed to to check a password solution with a computer at room
+;; temperature, assuming that reversible entropy computing isn’t
+;; realized and quantum computers have to stick to Landauer’s limit: A
+;; single bit-flip requires approximately 3 Zeptojoule[4] at room
+;; temperature, so we can flip 333 e18 bits per second with one Watt
+;; of Energy. Processing any information requires at least one
+;; bit-flip. Reducing the temperature to 1.e-7K (reachable with
+;; evaporative cooling) would theoretically allow increasing the bit
+;; flips per Joule to 1e30. That gives a plausible maximum of password
+;; checks per expended energy. Assuming that someone would dedicate a
+;; large nuclear powerplant with 1 Gigawatt of output to cracking your
+;; password, a 160 bit password would withstand the attack for about
+;; 23 years.
+
+;; [3]: https://en.wikipedia.org/wiki/Landauer's_principle
+;; [4]: http://advances.sciencemag.org/content/2/3/e1501492 "DOI: 10.1126/sciadv.1501492"
+
+;; With the password scheme described here, a password with 28 letters
+;; and 6 delimiters (172 bits of entropy) should be secure for almost
+;; 100,000 years in the Landauer limit at 1.e-7K, with the energy of a
+;; large nuclear power plant devoted to cracking it.
+
+;; With 24 letters and 5 delimiters it would only last about a month,
+;; though. Mind exponentials and the linear limit of the human
+;; lifespan :)
+
+;; However using the total energy of the sun (about 0.5e21 W), a 28
+;; letter, 6 delimiter password would survive for just about 5
+;; seconds. To reach 50 years of password survival against an attacker
+;; harnessing the energy of the sun (a type II civilization on the
+;; Kardashev scale[5] devoting its whole civilization to cracking your
+;; password), you’d need 200 bits of entropy. A 36 letter, 8 delimiter
+;; password (221 bits of entropy) would last about 100 billion
+;; years. With that it would very likely outlast that civilization
+;; (and its star).
+
+;; [5]: https://en.wikipedia.org/wiki/Kardashev_scale
+
+;; An example of a 28 letter, 6 delimiter password would be:
+;; GV7r!dcbm!venf,nGoH-MDjX,vBT8.1vWF
+;; Don’t use this one, though :)
+
+;; If you ever wanted to anger a type II civilization, encrypt their
+;; vital information with a 36 letter, 8 delimiter password like this:
+;; CB6d,D7fX-5sLV!mgCp,kTvG-He6n-7Fg9.REX3-r9F5
+;; keep in mind, though, that they might have other means to get it
+;; than brute force. And when they come for you, they will all be
+;; *really angry* :)
+
 
 define-module : examples securepassword
               . #:export : password yearstillcrackable
@@ -37,6 +103,22 @@ import
     ice-9 optargs
 
 
+define : years-to-crack-landau-limit-evaporative-cooling-nuclear-powerplant entropy
+       . "Estimate of the years needed to crack the password in the landauer limit"
+       let*
+        : seconds/day : * 60 60 24
+          days/year 365.25
+          tempK 1e-7
+          room-temp-fraction {tempK / 300}
+          guesses/Joule {1 / {3e-21 * room-temp-fraction}}
+          Gigawatt 1e9
+          guesses/second : * Gigawatt guesses/Joule
+          seconds/day : * 60 60 24
+          days/year 365.25
+          guesses/year : * guesses/second seconds/day days/year
+        / (expt 2 entropy) guesses/year 2
+
+
 define* : yearstillcrackable entropy #:key (guesses/second 100000) (number-of-devices 1)
        . "Estimate of the years it will take until the password is crackable"
        let