John Pomerat

23:52

So sigma sort of a homomorphism?

John Pomerat

24:05

is*

Calder Oakes Morton-Ferguson

24:17

Sigma obfuscates/encodes information - it is not a map between two groups

John Pomerat

24:46

Okay, I see, thank you

Calder Oakes Morton-Ferguson

31:12

Shoup’s original notation here was A(\sigma; 1, x) = x (EXTREMELY confusing, since A only gets the information of \sigma(1), \sigma(x))

Calder Oakes Morton-Ferguson

33:54

Only \sigma is probabilistic here, so O(.) makes sense in the usual way “in the variable m”

Cameron Musco

01:04:43

In response to tightening the probability bounds on polynomial roots, I might have misunderstood this question but: if you are looking at univariate polynomials over Z_p then I feel like you can't get better than d/p. You have d roots. So sum_{x \in Z_p} Pr(x is a root) = d. So at best, the max probability of x being a root is d/p. Of course if you restricted your attention to polynomials with less roots the point would improve.

Cameron Musco

01:05:15

bound* would improve

Calder Oakes Morton-Ferguson

01:07:09

Thanks for the great talk Nikki! The “Oracle” in this talk is particularly relevant terminology, what with the recent TikTok-Oracle deal in the news lately :P

John Pomerat

01:07:21

Thank you!

Rik Sengupta

01:07:22

thanks Nikki!

Rajarshi Bhattacharjee

01:07:30

thanks Nikki!