An excellent series and basic introduction to cryptography principles (albeit very basic). What I like best is not getting lost in the mathematical weeds of number theory, probability and statistics like so many overview intros into cryptography do. Anyone with a solid Junior or Senior HS year math background should be able to comprehend and grasp it, even if it does introduce some new concepts . . . or at least give a refresher on some that were barely touched on in prior math classes.
the 2nd flip of the coin in objective reality is not independent - there are measurable factors such as the weight of the coin on either side that could skew the probability that it begins within your fingers on one side or the other plus the physics of your bodily motion is measurable and adds additional probability that the coin will flip and land on a particular side
That is true. There are all kinds of small factors that may lead to one side being more likely every time. But, the 2nd flip is not in any way connected to the first flip. The metal is too hard and his fingers too soft to have a measurable effect.
What you're describing is an "unfair" coin and coin toss mechanism, and the result is a non-uniform distribution. Each toss however, is independent of all that preceded it. Even if he were able to perfectly replicate the toss from the same beginning state with an unfair process, you'd still get a random result skewed to a percentage heads and percentage tails that are not equal. It's a random distribution, but it's not uniform. Furthermore, you won't be able to predict with certainty what the next result will be from any of the prior results. The process is called a "Bernoulli Trial". So, if you have an unfair coin that will land 60% heads and 40% tails, the next toss will have the same probability as the last one, and therefore the 2nd flip is, indeed, independent of the first. Just because you get heads on the first does not change the probability of the result for the second. Look up "Gambler's Fallacy" in which a gambler bets that the next gamble or result will be determined by those prior to it for something like a game of craps or roulette. Each dice roll and wheel spin is a Bernoulli trial. Games such as poker or blackjack with finite decks have odds that change as the deck is used. It's still random but the probabilities change, thus they're not Bernoulli Trials. It's one of the reasons casinos use either infinite decks or at least outrageously large ones to prevent card counting - to make card deals and draws in blackjack as close to being a pure Bernoulli Trial as possible.
If a lottery was using a random number generator, how could i figure out the formula it was using to determine the numbers? Like how Eddie Tipton hacked the lottery.
There are numerous equations. Which is the most suitable depends on the purpose for the numbers and how they will be used. I built some in software decades ago using the equations for pseudo random number generators in the National Burau of Standards (NBS) Book of Mathematical Tables, a very, very large tome. I don't know if it's still published, but if so, it would be produced by the National Institute of Standards and Technology (NIST). Each of the pseudo RNG equations had constants that can be set and some discussion about its pros and cons with considerations and suggestions for selecting the constants. In some cases you're concerned about the period . . . how long it will run before starting to repeat itself. In other cases, spectral behavior will be important which are patterns that can occur before it starts to repeat. I suggest you find the NBS (now NIST) information or a similar source and explore the equations . . . and be certain to test what you select and its constants thoroughly (there are various tests described as well).
I didn't quite understand his answer to the question if true RNG are truly random [enough]. The way I see it, if you knew all the factors affecting a physical phenomenon, you can indeed work out what the outcome is going to be. However, "knowing" all about those factors entail the use of advanced enough technology which may not even exist yet, making it practically impossible; thus, it can be considered random "enough" (because it is practically impossible to predict)
The problem is more fundamental. It’s not just a practical issue that can be overcome with better technology. To any observer who is part of the universe themselves (like humans or technologically advanced measurement devices) the universe is fundamentally uncertain. See also Werner Heisenberg’s Uncertainty Principle. Important distinction: this doesn’t necessarily mean the universe is _truly_ random, or non-deterministic. Maybe it is, maybe it isn’t. But for us it is. For us it’s impossible to determine whether nature is deterministic or not.
I may die happy if people stop calling nondeterministic RNGs "true" and deterministic RNGs "Pseudo". This terminology is boneheaded, ill defined and use with different meanings by different people.
How would you call them? DRNG and NDRNG? (N for Non, D for Deterministic) Why is Pseudo so ill defined? I think it’s all right because even though it’s not really random, it serves the purpose perfectly and is indistinguishable from real (nondeterministic) RNGs.
@@stromboli183 DRBG and NRBG are terms defined by NIST. Deterministic Random Bit Generator and Nondeterministic Random Bit Generator. The DRNG term is Digital Random Number Generator defined by Intel for our RNG circuit that is built out of digital components. When you say "TRNG" what does "true" mean? Full entropy, or just nondeterministic? It is not defined. I've seen TRNG used to mean full entropy and non full entropy nondeterministic sources. Instead use "Full Entropy Source" to mean a source with perfectly uniform source of bits that are non connected by the internal state of an algorithm. "Non Full Entropy Source" to mean a source of not perfectly uniform data. "Deterministic" To mean an algorithmically defined random looking sequence and "Cryptographically Secure Deterministic Random Source" to mean and algorithmically defined random looking sequence for which it is computationally to hard to predict future and past values from seeing values from the source and for which the output is indistinguishable from uniform random data. Those terms are well defined mathematically and in English terms, whereas the definition of Pseudo and True used in PRNG and TRNG have been differently defined in many contexts. My book "Random Numbers, Principles and Practices" I go into the nomenclature in quite a bit more detail.
You are very misleading here. First of all - a coin or die flips are not independent if you are throwing them, they are only conditionally independent. And there is no reason why true random number generators are more likely to be uniformly distributed than pseudorandom generators. Uniform randomness is not a verifiable property of anything in nature.
An excellent series and basic introduction to cryptography principles (albeit very basic). What I like best is not getting lost in the mathematical weeds of number theory, probability and statistics like so many overview intros into cryptography do. Anyone with a solid Junior or Senior HS year math background should be able to comprehend and grasp it, even if it does introduce some new concepts . . . or at least give a refresher on some that were barely touched on in prior math classes.
I wish you were my teacher growing up
You make studying fun...
Wow, wonderful teacher
Now I can justify why it's the game's fault that I lost.
the 2nd flip of the coin in objective reality is not independent - there are measurable factors such as the weight of the coin on either side that could skew the probability that it begins within your fingers on one side or the other plus the physics of your bodily motion is measurable and adds additional probability that the coin will flip and land on a particular side
That is true. There are all kinds of small factors that may lead to one side being more likely every time.
But, the 2nd flip is not in any way connected to the first flip. The metal is too hard and his fingers too soft to have a measurable effect.
What you're describing is an "unfair" coin and coin toss mechanism, and the result is a non-uniform distribution. Each toss however, is independent of all that preceded it. Even if he were able to perfectly replicate the toss from the same beginning state with an unfair process, you'd still get a random result skewed to a percentage heads and percentage tails that are not equal. It's a random distribution, but it's not uniform. Furthermore, you won't be able to predict with certainty what the next result will be from any of the prior results. The process is called a "Bernoulli Trial". So, if you have an unfair coin that will land 60% heads and 40% tails, the next toss will have the same probability as the last one, and therefore the 2nd flip is, indeed, independent of the first. Just because you get heads on the first does not change the probability of the result for the second.
Look up "Gambler's Fallacy" in which a gambler bets that the next gamble or result will be determined by those prior to it for something like a game of craps or roulette. Each dice roll and wheel spin is a Bernoulli trial. Games such as poker or blackjack with finite decks have odds that change as the deck is used. It's still random but the probabilities change, thus they're not Bernoulli Trials. It's one of the reasons casinos use either infinite decks or at least outrageously large ones to prevent card counting - to make card deals and draws in blackjack as close to being a pure Bernoulli Trial as possible.
Great !
If a lottery was using a random number generator, how could i figure out the formula it was using to determine the numbers? Like how Eddie Tipton hacked the lottery.
Thanks
강의력 미쳤다.. 미국은 고등학생들이 암호학을 배우네 ㄷㄷ
thank you
12:08 True randomness to me is when it's proven that you can't calculate (not even theoretically) an outcome.
which is the best method to generate pseudo random numbers?
There’s much more to that if you really go deep, and it depends on the context. But the short answer would be: the Mersenne Prime Twister.
There are numerous equations. Which is the most suitable depends on the purpose for the numbers and how they will be used. I built some in software decades ago using the equations for pseudo random number generators in the National Burau of Standards (NBS) Book of Mathematical Tables, a very, very large tome. I don't know if it's still published, but if so, it would be produced by the National Institute of Standards and Technology (NIST). Each of the pseudo RNG equations had constants that can be set and some discussion about its pros and cons with considerations and suggestions for selecting the constants. In some cases you're concerned about the period . . . how long it will run before starting to repeat itself. In other cases, spectral behavior will be important which are patterns that can occur before it starts to repeat. I suggest you find the NBS (now NIST) information or a similar source and explore the equations . . . and be certain to test what you select and its constants thoroughly (there are various tests described as well).
I didn't quite understand his answer to the question if true RNG are truly random [enough].
The way I see it, if you knew all the factors affecting a physical phenomenon, you can indeed work out what the outcome is going to be. However, "knowing" all about those factors entail the use of advanced enough technology which may not even exist yet, making it practically impossible; thus, it can be considered random "enough" (because it is practically impossible to predict)
The problem is more fundamental. It’s not just a practical issue that can be overcome with better technology. To any observer who is part of the universe themselves (like humans or technologically advanced measurement devices) the universe is fundamentally uncertain.
See also Werner Heisenberg’s Uncertainty Principle.
Important distinction: this doesn’t necessarily mean the universe is _truly_ random, or non-deterministic. Maybe it is, maybe it isn’t. But for us it is.
For us it’s impossible to determine whether nature is deterministic or not.
Are you from teenage boss?
9:45 re
I may die happy if people stop calling nondeterministic RNGs "true" and deterministic RNGs "Pseudo". This terminology is boneheaded, ill defined and use with different meanings by different people.
How would you call them? DRNG and NDRNG? (N for Non, D for Deterministic)
Why is Pseudo so ill defined? I think it’s all right because even though it’s not really random, it serves the purpose perfectly and is indistinguishable from real (nondeterministic) RNGs.
@@stromboli183 DRBG and NRBG are terms defined by NIST. Deterministic Random Bit Generator and Nondeterministic Random Bit Generator. The DRNG term is Digital Random Number Generator defined by Intel for our RNG circuit that is built out of digital components. When you say "TRNG" what does "true" mean? Full entropy, or just nondeterministic? It is not defined. I've seen TRNG used to mean full entropy and non full entropy nondeterministic sources. Instead use "Full Entropy Source" to mean a source with perfectly uniform source of bits that are non connected by the internal state of an algorithm. "Non Full Entropy Source" to mean a source of not perfectly uniform data. "Deterministic" To mean an algorithmically defined random looking sequence and "Cryptographically Secure Deterministic Random Source" to mean and algorithmically defined random looking sequence for which it is computationally to hard to predict future and past values from seeing values from the source and for which the output is indistinguishable from uniform random data. Those terms are well defined mathematically and in English terms, whereas the definition of Pseudo and True used in PRNG and TRNG have been differently defined in many contexts.
My book "Random Numbers, Principles and Practices" I go into the nomenclature in quite a bit more detail.
I have a one of georgivs
I have a one of georgivs 1914_1914
One somaliland of hargaisa
You are very misleading here. First of all - a coin or die flips are not independent if you are throwing them, they are only conditionally independent. And there is no reason why true random number generators are more likely to be uniformly distributed than pseudorandom generators. Uniform randomness is not a verifiable property of anything in nature.