Introduction to Lattice Based Cryptography

*One technical note: At 1:30 I claim that lattices are composed only of integers. This is not true. Some lattices only contain integers, but in general, any rational number will do.

[nataliejarusewski]

About time I find a video that "dumbs" down this topic into information my brain can actually digest.

[armstronggaming]

DUDE, you just saved my whole physics assignment

[prashuprashanth]

Thank you for simple yet great explanation..

[Shounak]

Just what I was looking for. Thank You.

[macknightxu]

at 5:01, why e<<q/4? is it ok when e << q/2?
and why we need bit*(q/2) ? is it ok we have bit*(q)? or bit*(q/3)?

[macknightxu]

at 6:27, is the task provided point b, we need to find the most suitable s which is a lattice point so that s is the most closest point of lattice to b?
what is "a basis" here mean? why we here need "a basis"?

[_my_pobedim]

3:58 probably you mean a pre-image resistant hash function?

[randomvideos]

Hi, if b1.x = A.s.x + e1 .x, then how does it convert to b1.x = s.u + e1.x? we know that A.x = u, but does it mean we can reposition s at the beginning? won't it violate commutative property?

[macknightxu]

at 6:15, what the relation between this cryptosystem, LWE and lattice? Not even metion lattice here.

[quosswimblik]

owe well my method involving multiple ways to convert 1 integer into 2 or more smaller integers in a reversible way geometrically shuffling isn't in NP space either it can only do symmetric encryption and hashing.

[macknightxu]

is LWE problem based on Lattice? so that hardness of LWE problem is as hard as the problem of finding the suitable s in the lattice?

so i could conclude that this cyptosystem's security is based on the hardness of LWE which is basically a field of the lattice cryptography ?

[macknightxu]

Hi, at 3:50,
why each of its entries is a 0 or 1 binary, then Alice's X is "unique"?
at 4:05, why is x = (A^-1)*u actually a collision resistant hash function? the multiplication could not be done? why couldn't it be done?

[TheNomadic]

This may confuse some people at first. Here, we are talking about a lattice, which is kinda like a discrete module. Not to be confused with a lattice, which is an algebraic structure.

[randomvideos]

If A is a M*N matrix, then how come bob's secret vector S has M entries? wouldn't there be a dimension mismatch while calculating A*S?

[johnooe]

Yo I just completed algebra what is this lettuce cryptography you speak of?

[navjotsingh]

You never discuss the posets and how they relate to lattices. This video is great but it would have been nice for you to introduce that too.

[ThefamousMrcroissant]

Lattices are *often* scaled over the integers, but it's definitely not true that the elements of the vectors themselves are.

[fait]

taking exponential time on a QTM is impossible because it already is too exponentially powerfull

[mrv]

Downvoting... really bad narration. Reading from a script... but sounds as though he is like some junior high school student rushing through a passage that the teacher asked him to read in front of the class....