Posted on 08/17/2021 7:38:23 AM PDT by Red Badger
“You may enter any of ~128 characters as part of a possible password. That gives you the “one in a million” chance of guessing a 3-character password as you suggested. Thing is, most people (given the choice) will only use lowercase letters ... a search space of just 17,576 combinations, which means (in your 1 day halt after 10 bad guesses example) an average of 2.4 years to find the right key, vs your touted 300 years. “
That would be a really stupid security system and the guy that designed should be fired on the spot.
Obviously anyone in cybersecurity can do that calculation a priori. So if he’s designing a password security system why would he limit it to 3 characters and why not force the user to use more than just lower case letter.
If I was designing that system I would only allow passwords of say 8 or more characters and they had to include at least one upper case, one lower case, numbers and special characters. And if you guess wrong x times in a row you get blocked for a certain amount of time.
You can make that system for all practical purposes inviolate even by the fastest super computer. (Most secure sites today force you to do just that) (a system that would let you have 10 tries before blocking you for 10 minutes would require way more than the age of the universe to break it.)
Now you can reduce the “search space” by spying and surreptitiously stealing the password, which is basically what that story you referenced is mostly about.
It’s more a story on espionage than the breaking of a code.
Why stop? They should have kept going until the end.
Zero is not an infinity. Zero is one of the infinite set of integers (... -3, -2, -1, 0, 1, 2, 3,...).
In a decimal format it doesn't matter how many zeros (even an infinite number) are included in 0.00000... It is still the integer zero. Dividing zero by any real number (except zero) still gives zero, no matter how many zeros are including in the decimal format.
Any discussion of infinity is pointless, which is why in math infinity is instead referred to as “undefined”. There are an infinite number of points in an inch, so are there twice as many in 2 inches? The number zero is made up of an infinite number of zeroes just like an infinite number of points placed end to end is another point.
In mathematics, the discussion of infinity is certainly not pointless. The concept is used in calculus, infinite series, and in set theory, to name a few math topics. "Infinity" is not the same thing as "undefined."
Telepathic Intruder @64: There are an infinite number of points in an inch, so are there twice as many in 2 inches?
There are the same infinite number of points between 0 and 1 on a line as there are points between 0 and 2 on a line. Furthermore, as mathematician Georg Cantor showed in 1877, there are the same infinite number of points between 0 and 1 on a line as there are on a square defined by (0,0), (0,1), (1,1), and (1,0) on an x,y plane. Even Cantor was surprised by his discovery. A discussion of this is given in William Duhnam's Journey through Genius (1990), in the chapter, "Cantor and the Transfinite Realm."
Telepathic Intruder @64: "The number zero is made up of an infinite number of zeroes just like an infinite number of points placed end to end is another point".
Zero is an integer as well as a digit. You are confusing an infinite number of zero digits with the zero integer. The zero integer is equal to "0" no matter how many zero digits are included in the decimal format.
Heh— good one, bert! You have to imagine you have a cookie, sort of like the “imagining” of digital Fed Reserve money.
Reminiscent of the Beverly Hillbillies jokes about the character Jethro Bodine who “learned to cypher” (a mountain people term for calculation, multiplication tables memorization etc.). You may or may not recall this- from a long time back...but, for a laugh—
“Cipher something, Jethro”... and Jethro demonstrates his “goes intos” division tables:
https://www.youtube.com/watch?v=1H8e0MMwUec
Imaginary money (or is that cookie integers?) -— does that not have to ever be paid back to us, the People? As in billions the TARP program forced on banks by GWB’s Treas. Hank Paulson to cover the crash of realestate mortgage derivatives that were worth...nothing in reality (Paulson a former/current whatever VP at Goldman Sachs at the time!) Wells Fargo was forced to take over bad paper of Wachovia for example.
Zero cookies-— indeed, again... good one bert! Made the noon time!
It was Euler [1707-1783] who first speculated that transcendental numbers exist - that is, that not all real numbers are of the relatively tame algebraic variety - but the first example of a specific transcendental number was only provided by the Frenchman Joseph Liouville in 1844. When Cantor approched this subject in 1874, [Ferdinand von] Lindemann's proof that pi was transcendental still lay almost a decade in the future. In other words, as Cantor was developing his theory of the infinite, there were very few transcendental numbers on the scene. Perhaps they constitute the exception among the real numbers and not the rule....
Yet here was Georg Cantor confidently saying that it was the transcendentals that were in the vast majority, and he did so without exhibiting a single concrete example of a transcendental number! Instead he "counted" the points of the interval and realized that the algebraic numbers contained within were responsible for only a small part of this count. It was a startlingly indirect way to get at the existence of transcendentals.
Telepathic Intruder @67: Rather than pointless, I should have said nonsensical. The same infinite number of points? Really?
Yes, really!! And moreover, the real number points between 0 and 1 have the same cardinality (or one-to-one correspondence) with the real number points in any interval of finite length (see Dunham, p. 263).
In the same way, the infinite set of counting numbers has the same size (sometimes called Aleph-null) as the infinite set of even counting numbers (although this infinite size is smaller than the infinite size (sometimes called Aleph-one) of the set of real numbers).
In thinking about it from a finite perspective it does appear "nonsensical," but in the world of infinity it makes sense.
Now take your response and apply it, as it does, to an encryption system based on a poorly designed “random number generator”. The results are the same, albeit more subtle.
To wit: you made my point.
Yes I proved you’re nuts, and you should not be working at a cybersecurity job.
Only an idiot would implement a system based on a poorly designed random number generator with UNLIMITED bad tries. Is that what you would do?
Um, that’s what you did. I showed how absurd it is.
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