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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. |
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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 15:02, 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 |
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Organizer contact information
Brandon Alberts (blalberts@math.wisc.edu)
Megan Maguire (mmaguire2@math.wisc.edu)
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