How did the NSA hack our emails?

Professor Edward Frenkel discusses the mathematics behind the NSA Surveillance controversy - see links in full description.
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[angfu]

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

[Yoshiiro]

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

[gwho]

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

[VoDInnes]

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

[MrZphyrus]

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

[--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!

[utkn]

3:43 that unsuspicious grammar correction haha.

[boyinaband]

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

[soundlyawake]

My face during this video: O_O
My brain during this video:
My heart during this video: <3333

[Dombowerphoto]

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

[pThorpy]

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

[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!

[Nisstyre]

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.

[aroseland]

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!!

[marcschmidtpujol]

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 :).

[eskimo]

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

[benjaminbartholomew]

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

[RigelOrionBeta]

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

Fewer vs Less

[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..