Posted on 08/17/2021 7:38:23 AM PDT by Red Badger
Digits of pi are actually & provably random (well, have all qualities of randomness by any definition other than being part of a particular number). If I pick an unspecified and unguessable portion of pi, and arbitrarily scramble those digits up, the result is indeed random.
Otherwise you're faced with...
Calculating pie can be a challenge: https://www.spokesman.com/stories/1997/aug/17/wenatchee-apple-pie-takes-shape-hundreds-peel/
Oh, never mind.
The smallest infinity is zero, since it’s the sum of an infinite number of zeros. But can’t you just divide that by 2 to get a smaller one, you might ask? No.
Not inherently. Verification would be another process.
At any rate, Pi to that many places is pretty useless. It falls into the "how many angels can dance on the head of a pin" classification. I did it because IT can.
Why stop there? Keep going!
Next up: Guess a woman’s accurate weight.
Cheap enough on trivial computations that exceed the prior record of 50 trillion digits on a PC in Jan. 2020.
As to RNA analysis-— its a nice sales pitch, for something highly speculative and small demand. Speaking from a biochemical pharma clinical perspective.
Interesting they chose this as an example. As opposed to fluid dynamics or military applications, very life impacting.
“how many angels can dance on the head of a pin”
It’s not just a question I ask. I choreograph them.
(...software being non-corporeal entities that affect the real world, and which I create with little more than my mind and a glass slate covered with glowing dynamic runes.)
“If I pick an unspecified and unguessable portion of pi, and arbitrarily scramble those digits up, the result is indeed random.”
Couldn’t you do the same with randomly generated numbers. Start with that and then arbitrarily scramble them?
Actually it’s quite easy to implement cybersecurity. Simply limit the number of tries you’re allowed in a period of time.
If you’re odds of coming up with the correct key is one in a million, then waiting a day after every 10 bad guesses means it would take you on average 100,000 days - almost 300 years!
In other words it doesn’t really matter how fast a super computer you have. The time that it takes to decipher the code is dictated by the allowed interval between bad tries.
Pi to ten places = May I have a large container of coffee cream and sugar = 3.1415926535
I write security software. Ain’t that simple.
Any advantage in reducing the search space might reduce guessing time from eons to days - and yes such has happened.
Great historical example: https://www.mattblaze.org/blog/neinnines
Upshot: a broken random number generator lead to the discovery and killing of a Russian spy.
Other observations:
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. Sure, the user might make it more complicated, but knowing what humans would normally select as “random” biases the search to start with the most likely by far. Normal folk wouldn’t bother, but a government certainly would.
Next, you’re assuming the constraints applied will remain applied. Yes, your iPhone can be set to lock for a day after 10 bad attempts. Power it off after 9 attempts, resetting the counter, restart, and try again - no day-long delay. Someone built such a system (yes, addressing the obvious things I glossed over) and sold it to the FBI for million$, making it feasible to pound thru all possible 6-digit lock codes within hours.
Or I can bypass your “10 tries = 1 day delay” by breaking open the device and taking the storage chips out of it. Sure it’s still encrypted, but the hardware is known & documented, so I can copy the encrypted message out. Once so liberated, I can throw that data at a supercomputer (say, https://aws.amazon.com) and have it chew thru the possible keys. “One in a million” doesn’t mean much when I can try a million possible keys per second.
Sure “The time that it takes to decipher the code is dictated by the allowed interval between bad tries.” Sufficiently motivated, and leveraging whatever vulnerabilities I can discern, I can reduce both the time between tries, and the likely number of tries needed, by orders of magnitude.
In Carl Sagan’s book, “Contact”, he had a really interesting idea about PI. According to the book, there was a message embedded deep inside of Pi. Buried deep inside of Pi, in base 11, there was a large string of ones and zeros that could be structured to draw a picture of a circle.
Granted, that Pi most likely contains any arbitrary string of numbers, (I don’t think this has been proven) it’s actually likely that you could find something like this if you looked hard enough. Of course, the same could be said about ‘e’.
I have never ever used ‘e’.................
That post about Grahams number was insane.
// How would that be better than a randomly generated series of numbers?
How are you going to generate that random series of numbers? It’s actually harder than most people think to actually generate truly random numbers.
BTW, I would NEVER use digits of pi for encryption.
|-D
Yes, it is.
Hence my warning about needing a bucket for when your brain melts while reading it.
Someone worked it out:
If you have as many digits of pi as there are particles in the universe, there is a ~50% chance of any given 300-bit sequence showing up.
Oops, wrong π... 🤓
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