LSE Week 2015 - Day 3: Unlocking Prime Numbers with AKS Polynomial Tests 🔢

Programme :

Primality Tests and Factoring with the AKS polynomials - Robert Erra
19h30 20h30

Prime numbers are ubiquitous in modern cryptography and fortunately a lot of probabilistic and deterministic primality tests exist. The most famous is the AKS algorithm that has proved that “Prime is in P”, a result that has is one of the most important results in the last 30 years in computational number theory. On the other side, Factoring a large number is a hard problem whose complexity is still unknown. We propose here to analyse the following question: if we take a composite number what information can we obtain with primality tests ? We will explain how in some cases we can factor a number using primality tests ; we will for example explain why Charmichael numbers are easy to factor and we will finish with the presentation of a new (and curious) factorization algorithm that use the AKS polynomials, the algorithm is not efficient but it is deterministic and can still be improved.


Draw me a Windows local kernel debugger - Samuel Chevet & Clément Rouault
20h30 21h30

Our journey to automatize some local kernel debugging without the use of Windbg. We will explain how dbgengine (core of Windbg) works: which API are exposed and what does it require to work properly. Finally, we will show how to abuse it to be able to perform local kernel debugging in Python.


Execution trace and memory analysis - Matthieu Tardy
21h30 22h30

When reverse engineering, optimizing, or debugging a binary, one could often use an overview of the changes happening in memory. This talk will introduce a memory analysis tool based on pin, cover how this tool is implemented and show some of its use cases.