NTSGrad/Abstracts: Difference between revisions

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| bgcolor="#BCD2EE"  |  The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.
| bgcolor="#BCD2EE"  |  The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$  to find $n$.  
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$  to find $n$.  
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.  
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.
 
This is a prep talk for the Thursday seminar 9/15/2016
This is a prep talk for the Thursday seminar 9/15/2016
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Revision as of 20:02, 12 September 2016

Sep 06

Brandon Alberts
Introduction to the Cohen-Lenstra Measure

The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.


Sep 13

Vlad Matei
Overview of the Discrete Log Problem
The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.

In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.

This is a prep talk for the Thursday seminar 9/15/2016


Sep 20

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Sep 27

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Oct 25

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Dec 6

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Dec 13

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Dec 20

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Organizer contact information

Brandon Alberts (blalberts@math.wisc.edu)

Megan Maguire (mmaguire2@math.wisc.edu)

Bobby Grizzard



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