Author Archives: incertia

Cheap Nullstellensatz

I was recently asked to prove a non-exhaustive set of cases for the weak Nullstellensatz, and the proof was so deceptively simple I decided to share it. The main theorem goes along the lines of this. Nullstellensatz: Let be an … Continue reading

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ISL 2017 A1

Problem A1: Let and be positive integers such that     If , prove that the polynomial     has no positive roots. Solution A1: We appeal to a similar strategy that is used in IMO 2012-2. Write     … Continue reading

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IMO 2018 Day 2

Day 2 had a bunch of really nice problems with more advanced techniques required to solve them. Problem 6 is also hard and I will be writing it up at a later time. Problem 4: A site is any point … Continue reading

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IMO 2018 Day 1

I have solved problems 1 and 2. I have not yet attempted problem 3 but I believe that it is beyond me, especially within a time frame of four and a half hours. Problem 1: Let be the circumcircle of … Continue reading

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I finally released a thing

It’s a small tool to parse Unity3D TestResults files from testing in CI/CD environments, but it’s a tool nevertheless. You can find it at https://hackage.haskell.org/package/unity-testresult-parser.

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Revenge of the Finite Fields

A few days ago, I posted some proofs and a construction of finite fields. It turns out there are a lot more nice constructions and proofs and problems related to finite fields, so I’ll be sharing some of them here. … Continue reading

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Finite Fields for Mortals

I’ve been studying a bunch of cryptography lately, and I thought it would be nice to present finite fields in some relatively easy to understand way that doesn’t require too much prior knowledge. All that is really needed here is … Continue reading

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UIUCTF2017 – uiuctfsck

This was a brainfuck interpreter that let you print out some internal machine state. Notice that the interpreter does not like it if we have the string “machine” in our format string. We examine the machine object, and notice that … Continue reading

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UIUCTF2017 – OldTV

Not many people solved this despite the author and I believing that this should have been an easy challenge. We were given the following program: Initially, you should try to verify the signature and compute , and realize that it … Continue reading

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Codegate 2017 Prequals – BabyPwn

This was a straightforward ROP challenge, which was made difficult on our side due to bandwidth issues. Interestingly enough, every time we tried to leak the stack cookie it started with a null byte. We have a read primitive (actually … Continue reading

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