How did the NSA hack our emails?

[@numberphile]

Check out the video description for more information and links - and here is some extra footage from the interview which is pretty cool - kzbin.info/www/bejne/Z4CZaqh4gZdlpLs

[@tenpermental]

I just bought Love and Math and cant wait to read it, I love all of your videos and wish there were enough hours in the day to watch them all. Thanks!

[@angfu21]

I can't believe the NSA is reading my email. I don't even read my email.

[@fluffylinen]

q

[@anitatromp6295]

Imagine how much spam they had to go through.

[@jeffavella5094]

Right? I wish they'd delete my smam and mark the important stuff for me.

[@Soulsphere001]

They generally only read emails with specific keywords.

[@palt7036]

@@Soulsphere001 woooosh

[@gwho]

They find the most likable, eloquent, curious professors on this channel.

[@vanya25_n]

true

[@Yoshiiro]

"There are less solutions ?" "Yes, there are fewer solutions." GOLD

[@redbeam_]

can you explain that please? im not a native speaker

[@AdamW655]

redbeam_ "fewer solutions" is the convention in the English language to my knowledge of it. "less solutions" is a common error that is to some people ( like snobs) something that makes one look sily. some people like to point out this error and correct it, maybe to look more sophisticated. It was amusing because Edward's use of "fewer" is grammatically perfect, while the native speaker got it wrong.

[@denismaximov8902]

I think non-native speakers are better grammarians. They understand the language better and they rely on their knowledge and not intuition like native speakers often do

[@NearbyTowels]

+redbeam_ To be more specific, 'less' is used to denote a reduction in an indefinite amount, such as of a substance. If you have a glass of water, and you pour some out, you now have less water. 'Fewer,' on the other hand, is used for distinct things which are typically countable. If you have a number of oranges, and you give some away, you then have fewer oranges. It is a largely pedantic distinction, but I, too, enjoyed a non-native speaker using the more correct form.

[@danguee1]

Blimey - 'less solutions' sounds actually quite dim (and we know the film-maker is not the brightest button in the box!)

[@4pThorpy]

Ah ok, it's all done by clocks in some villages in Australia, I fucking knew it

[@VoDInnes91]

This was the best Numberphile video yet, hopefully Professor Frenkel will make more appearances, I could listen to him explain things all day!

[@utkn]

3:43 that unsuspicious grammar correction haha.

[@MrZ3phyrus]

Ah man Frenkel is a boss. I had 2 classes with him while at Berkeley. One of my favorite professors. Really interesting video.

[@boyinaband]

Frickin' fascinating, I wonder what the relation between the numbers is

[@Friek555]

Did you mean fookin' fascinating?

[@Friek555]

It was an allusion to Daveo, an imaginary character in BIB's videos who adds "fookin'" to every sentence he says.

[@castroski7]

Boyinaband lol whatcha doing here

[@joshuamitchell5530]

He made a video about how we basically shouldn’t learn maths in school because it’s useless and here we are.

[@___xyz___]

Boyinaband Can you please go be pretentious elsewhere?

[@Nisstyre56]

Title is kind of misleading. The NSA did backdoor a PRNG based on elliptic curves, but as far as anyone knows it wasn't widely used to encrypt emails. Emails get encrypted in transport using SSL/TLS and (if you bother) with PGP or GPG locally, and the most popular implementations of these don't use this PRNG. There might've been some people using RSA (the company) products to encrypt their emails I guess though, but it seems unlikely. The NSA was able to get access to emails by tapping data-centre links where the traffic passed through unencrypted, and by getting court orders that forced companies to hand over the plaintext or SSL keys.

[@stanislasb.6880]

His accent is EXCELLENT !

[@spitlerspitler]

wow that example for modular arithmatic with the clock is fantastic, thanks!!

[@--Lam]

I absolutely LOVE how a guy with an awfully thick accent casually corrects a native speaker that there are FEWER, not less solutions... only at 3:40 here. It's like myself talking to Brits and even Indians, they think I'm an idiot based on my accent and I think they're idiots based on their actual knowledge of English. This is so heart-warming!

[@xTurqz]

Lam there is no correct one. The correct one is the one that people use, that’s how language works. That’s also how language evolves over time other wise you could say that the entirety of the English language is wrong. Stop trying to be smart.

[@shreyanshpurwar9039]

THICC accent

[@Dombowerphoto]

Russian accent saying. "Zillions and zillions" is awesome.

[@rawr51919]

It's XD.

[@WellingtonBikeCam01]

Russian accent explaining how the US govt spied on... Everyone.

[@Dombowerphoto]

1:50 (for your reference to just keep playing it over and over for zillions of times

[@gregaizi]

Do you think that this math research funded by Russian government? Fully or in part?

[@robertthompson7059]

@@gregaizi Would you be mad if it were? Would you rather hunt for the messenger or would you just ask yourself the simple question? "Have i just been screwed over by my own government systematically along with a quarter of the Planet or more?". And really now, could you corrupt the logic? This is not the kind of stuff that needs funding or that could be twisted left or right, this either is possible or is not and it seems damn possible to me since all it takes is 1 detail to be compromised and the whole point of the encryption flies out of the window and whoever has put that detail there owns your privacy and mine. It doesn't matter who we blame or who we don't, simply the fact that an institution has done this and made it a standard and then set it as a REQUIRED standard, is already a tragedy while the required transparency was not even offered after requests, which as far as i know, it HAS to be public, otherwise it serves no purpose and trust is inexistent. I could say a lot of things and be right and wrong after all but your presumptive question sounds more like a witch-hunt or "look at the tracks" vs "look at the wolf" scenario at best and you're the one chasing accent over factual scientific evidence based on pure testable logic and proof.

[@benjaminbartholomew]

I'd love to see a video about the math behind #Bitcoin, to continue the discussion of cryptography.

[@eskimo227]

when he said the govt provided the equation and the variables, I knew exactly where this was going.

[@marcschmidtpujol550]

They showed me congruence equations at university on monday... I was wondering all day long why it made any sense to learn that. Thanks to Numberhile I am more motivated to go on in class :).

[@clixbits]

We have enjoyed watching these videos as much as you have enjoyed making them. I'm looking forward to an exciting new year of Numberphile videos..

[@Ubersicht]

Sneaky, sneaky government. Next time they say: "hey you don't have to do all that work, here, we did it for you" The answer should be: "Thanks, but no thanks"

[@nelsblair2667]

American tax dollars were used to make Americans less secure. It happens every day. No American wants this. That’s why government agencies do it secretly. The impressive part is that there were no jail sentences handed down. No one stopped trusting the very agencies, which undermined our security. These are enemies of America. They are traitors. The law is clear, regarding their sentences. Enforcement is absent. We can rely on government to use our tax dollars to undermine our security. We can’t rely on government to bring these individuals to justice.

[@silentelysium]

Thanks Prof. Frenkel for the excellent and simplified overview to the maths applied in by the NSA to hack our emails. It just found it so fascinating and I was pretty much glued to the screen paying attention!

[@jmills4313]

The EXACT same backdoor used in the Sony pictures hack too. And when he said it's all puic information he meant that very literally...the source included which has always been public (they had no choice...rsa is opensource).

[@SpinningSpinor]

On the whiteboard, he was doing some calculations in string theory. Probably W-algebra.

[@SpinningSpinor]

And I saw the Galois group.

[@jimstantinople]

y'know, some light number crunchin

[@HaouasLeDocteur]

As soon as he began talking about Elliptic Curves, and seeing as the title mentions NSA, no doubt: this is going to be about Dual_EC_DRBG.

[@tkm2210]

Nice touch with the eye on the "i" in numberphile.

[@fileeditfileedit]

I think the imaginary "i" would've been cooler

[@aroseland1]

I found this interesting despite the fact that i didn't understand any of it.

[@Coachcell]

I must say, although I probably fail embarrassingly in comparison with most of your subscribers when it comes to mathematics, I LOVE NUMBERPHILE!!! Keep up the great work and keep these great educational videos coming!!

[@TheBlueToad]

Did anyone else get that Watch ad, and noticed that it was set to 10:10

[@RamsesTheFourth]

nope...adBlock+

[@labrynianrebel]

That 10:10 watch ad thing has ruined my life >_

[@HenningRogge]

The content of the video is really good, but the title is misleading. Weakening the design of one of the NIST random number generators has not much to do with how the NSA is reading emails. Fact is that most emails are unencrypted... and their metadata cannot even be encrypted by the email sender and receiver.

[@soundlyawake]

My face during this video: O_O My brain during this video: ¿¿¿¿¿????? My heart during this video:

[@macrameschool]

I cannot believe it :(

[@paulgilbert2506]

3:44 Love the way he subtly corrected the interviewers grammar.

[@watcheem]

I live and Sweden and we don't use AM or PM, we say 14:00, 18:00 and so on :P

[@Kdrzewinski]

This is nice, but I kinda miss Dr Grime. When will we see him again? I loved how passionate he was about all these numbers.

[@RigelOrionBeta]

3:40 A Russian correcting a native English speaker on grammar, haha Fewer vs Less

[@aislingoda6026]

implying there's one correct grammar

[@CarbonRollerCaco]

Native speakers tend to be less picky about grammar than foreign speakers because they generally know better what's close enough to widely understand. They ARE the standard, after all.

[@segmentsAndCurves]

@@CarbonRollerCaco technically the truth.

[@MrDucktaper]

I'm right now studing for an exam about modular algebra and all this RSA stuff. Numberphile delivers.

[@Ubeogesh]

hate AM\PM clock

[@SrmthfgRockLee]

Indeed. Whenever I hear about some meeting.. whether concert or something else/whatever... I can accept anything & I like the darkness/night more, but I know people are more specific so when they say be there at 3:00 (and most people don't even write/type/say the PM but mean it most of the time) so I'm like Wtf :O people actually go & organise at those times in the night?! So confusing... common sense doesn't often work in this case.

[@robertthompson7059]

@@SrmthfgRockLee Common sense should dictate that it would be common and that people would use it/practice it. People assuming that you will assume the correct half time of the day are just the kind of people that would shoot you thinking you were gonna shoot them first or something like that. It's a disaster to have such a way of thinking among Humans these days, it's unacceptable to be so dependently assumptive and enforce it onto others by default and it could only be a problem (more often than not) if you are the one who doesn't think like they do. No wonder religious and anti-religious nonsense peaks the top on the last few decades, it's not the freedom, it's just the false sense of confidence in the individual nonsense and it being forcefully pushed and accepted irrationally under no justifiable circumstances.

[@Bazo1337]

This has got to be the most interesting video that I've seen in a very long time. Thanks.

[@ThoolooExpress]

That is why I like RSA encryption: No tricks, no traps, and understanding how it works makes gives you no back doors.

[@tkandme3]

Lol.

[@ThoolooExpress]

***** While there are limitations to it, it is a mostly effective, but simple and straightforward cryptosystem. It is well known how it works, so it is impossible for the NSA to pull something like they did. Of course, it necessitates very large public keys, as well as being completely vulnerable if you have enough computing power to devote to it. (Which the NSA probably does.)

[@elapplzsl]

***** not the RSA company, I think he is talking about the encryption method.

[@JUICEPPL1]

Sorry mate hes dead serious.

[@GladerDev]

***** Lol, do people often mistake RSA the company and RSA the encryption technique?

[@mercuryboycyano]

Very interesting video. I loved the bit about "clock arithmetic" & the random number generating. A takeaway from this video could be midern society using decentralised encryption generators.

[@Ashbi71]

i didn't understand! :'(

[@Hythloday71]

Frenkel, this guy is ace, super cool, his Multivariable calculus online lectures are top !

[@WTFitsAmuffin]

Well I live in traralgon, safe to say thay blew my mind.

[@galesx95]

This video was fascinating for me because I'm going to study computer engineering (I don't know if you call it that in US or UK) and I'm lookong forward to study all this things!

[@LoffysDomain]

Prof Frenkel and prof. Martyn Poliakoff from the Periodic Videos KZbin Channel got to be among to best pedagogues living. Smart + motivated to teach _and_ well structured and able to enthusiastically teach their stuff. Clone them :-)

[@lulila3000]

Love this channel. They are able to explain "complicated" things in the simplest way, (an ability I wish many of my professors had), they make mathematics look so easy haha. Only if you understand something completely, you are able to explain it simple, and that's why I admire these people quite a lot

[@sergyu123456]

That accent, though. I could hear him talk all day. xD

[@zxxczczczcz]

xD

[@leNNy5655]

I find these videos about encripting and similar things the most interesting.

[@KatieRabbitt]

Love these videos. It seems many people fear the NSA, and think they have so many secrets, but really, most of it is public. I always love when people mention NIST too. NIST and metrology is a little known, but really cool branch of science and math.

[@robertthompson7059]

"It seems many people fear the NSA, and think they have so many secrets, but really, most of it is public." Wait a second, what? You must be talking about NASA, that's a whole different agency and it's a civilian one, while NSA is a policing service practically to put it brutally simple. They're one of the most secretive agencies there are and that's just from the ones admitted to exist, we barely have a clue or two about those hat MIGHT exist and we're not told about but they are processing our data and information on us 24/7.

[@EricFontaineJazz]

Great explanation. Just the right level of technical depth for a youtube. Title is misleading as NSA used other methods for hacking emails, as elliptic curve encryption is not commonly used for email.

[@RSP13]

I still don't understand one thing: If supercomputers are capable of finding primes MUCH bigger than those used in cryptography why would be difficult for those computers to find the primes of a 1024 bits key? For example: in 2013 was found that 2^57885161-1 is prime and that number is huge (17,425,170 digits), much bigger than the primes used in cryptography, which are about 2^1024. ("only" 308 digits). I am confused.

[@joshualowry3466]

It's easy to generate, but extremely difficult to unscramble.

[@majoro7251]

Bunny83 thanks for the explanation :P Bunny from UA? :o If that's you: me and my icon loader are following you everywhere xD jk it actually was a coincide that I'd seen your comment here, thanks for the insight :) I wonder if the usage of bit shifting would somehow cut corners when factorizing numbers cuz that's what I used to do back in ACM to figure out number of zeros in a big non-primal 10^x number.

[@robfletcher8762]

RenanzinhoSP Because you look at the prime and you need to figure out what X x Y is

[@rawheas]

+RenanzinhoSP its not solving for the prime number that is hard, its a function that is known as a mathematical trapdoor. This means it computes in one direction much easier than backwards. It just takes in a large prime number in order to do that. It is a very simple idea, for example finding 887*523 is far easier than finding the factors of their product. So the algorithm he has here simply takes large prime numbers in so that the complexity of solving the problem backwards is so large that a computer can't even try all the possibilities. he very much understated how complex the solution is, with current technology all the super computers in the world couldn't crack a 128 bit encryption, even if they had years to work on it.

[@RSP13]

+Brandon Denning Thank you

[@CaroleMcDonnell]

Oh my gosh, I totally understood all that! Thanks guys!

[@SiddharthMusic-uj8ox]

The title is misleading.... it should be "How the NSA is still hacking you emails?"

[@infinite1der]

This follows along the lines of chosen "weak" S-boxes in block ciphers (DES). Knowing the relationship between P and Q (and the resulting PRN) gives the attacker an advantage when performing cryptanalysis. Just because the relationship may (or may not) be known doesn't mean that the NSA is "hacking our emails". This simply suggests that they have an advantage in doing so...

[@GtaRockt]

In some European countries we actually say "14:00 o clock" for 2 o clock in the afternoon.

[@TheStevenWhiting]

Lobster with Mustard and Rice That's just called a 24 hour clock time, in America known mostly as military time.

[@robin-vt1qj]

every country in europe*

[@EngineeringNibbles]

+Michael Adsetts french and others ( non english ) do

[@GamesFeeder]

Britains are no longer Europeans. German says 14.00 o Clock (14 Uhr)

[@warpman345]

economically maybe, but they are still europeans

[@kd1s]

Just a small correction - email doesn't go encrypted at all unless you encrypt the BODY of the email message. All email goes open on port 25 from server to server.

[@WellingtonBikeCam01]

You can run encrypted SMTP on a server. If both sender & receiver mail-server are using it, then you've got strong point-to-point encryption while the email is in transit between servers. I guess it might not be a good idea to use ECC encryption, though ;)

[@rich1051414]

Not necessarily. When you check your email from a browser, from say gmail.com, they encrypt your connection, so any email read would be pass to you in an encrypted state. The point is, the NSA more likely than not, can see right through the encryption, because so many used the pre-backdoored algorithm inputs they provided the public. As explained in a previous video on computerphile, the unpredictability in the randomness of a 'salt' in an encryption algorithm is its foundation. With that block removed, it falls apart.

[@Caobilll]

Why is the title of this video past tense? Should it not be how DOES the NSA hack our emails.

[@LiamPorterFilms]

3:43 it almost sounds as if the guest is correcting the interviewer’s grammar, here!

[@listocalisto8124]

In germany we actually say 14:00 o clock. it goes up to 24 o clock, and then starts again from 0 o clock. we don't have am or pm. it's just 0 to 24

[@5thDragonDreamCaster]

Wu Tang That's how it should be everywhere.

[@listocalisto8124]

5thDragonDreamCaster yeah, it would be much easier. sometimes when i read pm/am i first have to think what that means. here you clearly know the difference between 06:00 o clock (06:00 am) and 18:00 o clock (06:00 pm)

[@5thDragonDreamCaster]

Wu Tang And what kind of measurement name is a "foot", and 12 inches, what did the people who invented it pull hairs out of their asses and count them for the numbers.

[@5thDragonDreamCaster]

Wu Tang Next they will make it 3 and one third or something.

[@CutiePi]

Wu Tang I use both I know both systems I like both systems gg me.

[@platipusoj]

If anyone is interested, the reason he says the best modular systems are prime is because they fall into the definition of a mathematical field, which has a bunch of usefull properties. You can read about those in wikipedia, or learn about them in linear algebra

[@JohnMcclaned]

Hey Numberphile! What would be the easiest way for me to privately contact you guys?

[@numberphile]

Depends on who does your encryption?

[@JohnMcclaned]

Numberphile My seed!

[@DanielGallagherMusic]

This is one of the coolest numberphile videos I've seen..... But they're all awesome.

[@mememe84]

Ok so why don't people come up with their own P and Q numbers , this way no one will know the relationship between the two numbers and you have security with no backdoors?

[@kujmous]

Luckily I have my own ASCII encryption module. Kinda proud of it, really. I never was very confident on prepackaged encryption processes.

[@laszlofoldi6030]

I'm really sorry to mention, but I found a mistake in your video. If you talk about (mod x), you cannot use the number x itself, only 0

[@the_blahhh]

Yea, in CS that matters, but 1-12 is just as valid as a residue system (modulo 12) as 0-11. 12 is literally equivalent to 0 modulo 12, as opposed to not being allowed. So the essence of the mathematics doesn't change, although the implementation does.

[@DepModMuffin]

He started off with the clock and the way we calculate the time as an example for lay-people and continued with it for the sake of convenience.

[@Hythloday71]

ohgeedubs Yea. 12 becomes the additive identity, provider of identity operation, which is all that matters really for group structure.

[@DeathBringer769]

The personification of "knowing just enough to be dangerous..."

[@LabaShabba]

So glad I've found this channel. Some of the most interesting topics around. Keep up the good work and have a good xmas.

[@thrustvectoring8120]

"why do we say 2PM and not 14:00?" Because you are british and use 12 hour time format instead of 24 hour time format?

[@alandouglas2789]

You're simply using mod 24 instead of 12, I think you've missed the entire point of this video

[@JesseGilbride]

thank you, thank you, thank you for this! this sheds some light on the topic that would otherwise have been much harder to discover.

[@TechLaboratories]

So, in summary, the NSA didn't 'hack' the actual information so much as manipulate the processes of generating the information in a way that they, and only they, could accurately predict the results of what is supposed to be a pseudo random processes. It's hard to be livid and incredibly impressed at the same time!

[@dingaia]

Yea I want to know how they figured it out! Talk about incredible. I'd also like to see more in depth of which companies are using it and several points about how bits are encoded into the algorithm.. truly marvelous indeed to know there was a backdoor, and what are these companies doing now that the code is compromised.

[@MadaxeMunkeee]

Digital Encryption is mathematically proven to be impossible to crack with current technology when implemented correctly. Not even the NSA can hope to do it. So this is really the only way that they can 'crack' any modern code, by tricking people into implementing it incorrectly.

[@dingaia]

***** , So because they knew the variables involved they were able to figure out the relations between them? I still don't believe I'm full grasping what's going on here. They told people they have encryption but it's not really encrypted because they know how to decrypt it?

[@MadaxeMunkeee]

***** Well I kinda implied that when I said 'with current technology' but yes, it's intractable not impossible. Also when we say 'crack' we mean 'do better than brute force', and that certainly is impossible with current technology.

[@MadaxeMunkeee]

dingaia It's not so much because they knew the variables, because the values of P and Q are public information so knowing that doesn't give you an edge on anyone else. The NSA had an advantage because they were able to select the values for P and Q in advance, and so they chose them to be connected in such a way that they could predict the outputs of the random number generator. Other people can't easily identify the specific manner in which P and Q are related (and the only reason the NSA know is because they selected for it in advance) so they don't have that extra information. So people are still safe from each other when they use the encryption algorithm the NSA gave out. They just aren't safe from the NSA.

[@noxiouspro]

I like how he make an analogy of modulo.

[@Fenrakk101]

Really upset at 9:20 that the NSA logo wasn't animated to gobble the numbers like PacMan :C

[@robertthompson7059]

Lol, i should seen this coming, i didn't even think about it though. Now makes me wonder how funny it would look.

[@ElloetteLightbringer]

Less solutions???! So glad he corrected you on that one!!

[@LazoeJSCREI]

Edward talking about NSA, coincidence? I think not jk

[@anom2492]

Illuminati confirmed?

[@Luisitococinero]

Waiting for a comment sort of this.

[@DominoPivot]

Reminds me our RSA encryption math class, and my friends safe password system :)

[@DocWolph]

1:57 But Megamind is a good guy... (Sad face)

[@kaikarius5678]

I hope my comment pushes this excellent video! Very well done, please do keep up your outstanding work.

[@andrewcrawford2977]

I love the way he makes his x's.

[@00bean00]

Haha, that's how they were done in ex-Soviet schools, too

[@FishKungfu]

I love love LOVE this stuff!! More of Dr. Frenckel, please!

[@TimmacTR]

A russian guy talking about mathematic encryption...so cliché.. :)

[@GraveRobbertt]

Wait, what? This is a cliché?

[@Nilguiri]

3:43 Yeah, Brady... there are fewer solutions, not less. Solutions are countable.

[@Clint945]

So after losing his hand and his sword-fighting skills, Jamie Lannister took up mathematics instead.

[@SyedRizvii]

so far the best and math invoking video....loved it!

[@yuriyolean8504]

No, no, no don't thank us - we thank you

[@ksec27]

best numberphile video(s) ever!!

[@CoffeePoints]

I like how there are just random equations in the backboard, that serve no purpose whatsoever except to make it look smarter XDD

[@00bean00]

Or this is just his classroom/lecture hall?

[@popodood]

i am familiar with most of the math on this channel, but i get lost when there is coding and computerphile stuff. I want to learn how computers and internet works

[@GTelo23]

But if they can predict the outcome, it means that the numbers are not that random!

[@MadaxeMunkeee]

True random numbers are hard to generate on computers (read: practically impossible). For encryption to run efficiently, people usually turn to pseudo-random number generators that run much faster on computers, and are usually (except in this case) cleverly designed so as to make it as difficult as possible to distinguish the outputs from random.

[@numberphile]

MadaxeMunkeee indeed --- Random Numbers - Numberphile

[@ColossalZonko]

not even humans can generate a random number..

[@Poldovico]

Batman You can use sensors pointed at white noise. Random.org for instance uses the electromagnetic background noise of the universe.

[@ColossalZonko]

Poldovico that's random enough, radiation form radioactive atoms is even more random though.

[@StewieGriffin]

i have 10 emails and i have a tough time trying to understand which email should be my real one

[@chrisofnottingham]

Lol, 3:42 Brady get "less" corrected to "fewer" :-)

[@calebmallen]

I'm not exactly a "numberphile", so the knitty gritty details of this pretty well go over my head, but I think I get the general idea, and I find it fascinating. Question: if one were to generate a new P and Q, would that thwart the efforts of the NSA?

[@jmills4313]

Yes it would've...this has to be done by the integrator or whoever compiles it I believe. I do know that back then if you changed p & q your device or application would not recieve fips 140 validation. P & q had to remain exactly as they were set originally...which alone is extremely suspicious.

[@taiming71]

Never under estimate the laziness of people. When it comes to doing work. Copy paste, don't upgrade operating systems, use the numbers some one gave you. It is no wonder hacking is so easy these days vs data bases. The people operating them are just doing the bare minimum to protect them.

[@Jsuarez6]

Just ordered the book from Barnes and Noble!

[@xTotalGhost]

Yep fell asleep just like math class

[@NikopolAU]

You have the right to remain stupid. Everything you don't understand can and will be used against you. Most likely for profit.

[@xTotalGhost]

NikopolAU watching this at 3 in the morning i dont have that long of and attention span

[@robertthompson7059]

@@xTotalGhost Lol, then you seem to be excused, but please make sure to watch it after you wake up too, even now 5 years later, just saying. I always watch this stuff to fall asleep to and then make sure to watch them all again after i wake up, just to make sure they've gone through all my filters.

[@jakebricker697]

seeding each number with beginning index 0 will always yield the same output; always make sure each iteration of the seed is not necessarily the previous iteration of the seed, ipso extendo seed(n) != seed(n-1)

[@dipro001]

His accent sounds so intellectual! lol.

[@00bean00]

With British instruction

[@darius-hollard]

Really good video !! I don't normally enjoy maths but you guys tackle great subjects and explain it well.

[@ProdigySim]

Very sensationalistic title.. the Dual_EC_DRBG RNG was already suspected to be backdoored (or backdoorable) since 2007, and InfoSec specialists have been advising against using it since then. The only known use of Dual_EC_DRBG RNG was RSA (the company) who set it as a default RNG in one of their redistributable libraries--and it has been revealed that they were paid to do this. Hacking emails is a completely unrelated subject, and there's no evidence I've read that Dual_EC_DRBG RNG was a part of any major NSA winning. I don't know if I can link articles in here, but check Ars Technica for references. They've been covering the technical side of the NSA debacle religiously and accurately. I'm really disappointed by the misinformation spread by this video.

[@browncoat697]

I think Numberphile was simply using this particular random number generator as an example, and not saying "the NSA backdoored this algorithm and uses it to hack your email!"

[@JacobManson]

Exactly, I think it is far more important to make it known that nothing of this sort would need to be done to "hack" email, as email is nearly always sent in the clear, meaning anyone that has access to the lines connecting 2 servers together (ie NSA), can simply read any and all email going across them.

[@joories]

Realy love the encryption videos.

[@Garbaz]

we in germany say 14 and not 2 pm :D

[@powmod1]

That's how it is in most of Europe.

[@EGIL94]

We say 14 in Norway to :))

[@Garbaz]

KlaxonCow i know i know

[@vascohenrique]

In Portugal as well.

[@DamianReloaded]

In Argentina we use 12 most of the time, but when we want to make clear if it is am or pm we use 24.

[@jinglebots]

wow thank you for making this. a service to all of us

[@phatcatrat]

The NSA did not hack emails at all. They simply asked various companies for their users' data, and they complied. Regardless of the legality of this action, no hacking was involved.

[@GhostInTheShell29]

Simply asking works well when dealing with companies like google, yahoo. Or even countries like Canada, and most of Europe that gladly handed over personal data on all their citizens, or customers. But when the NSA needs information from Iran, China, Venezuela, Or from a South American telecommunication company it can't ask, it be a security risk to ask even if they did say yes and it hacks instead.

[@hacelocononda]

Is there any evidence supporting that claim? Not that I find it anywhere near strange, but some backup info supporting the fact would add to the discusion.

[@phatcatrat]

Billy You can read about it if you like.

[@GhostInTheShell29]

Billy The Snowden leaks, pretty well covers it, and he gave documentation.

[@jhyland87]

@numberphile - This definitely got me to purchase Love and Math... Thanks!