Hello everyone!

I thought that some of you may be interested in the online CRYPTOGRAPHY olympiad — NSUCRYPTO 2018, which will start in two days.

You can have a look at problems from previous rounds.

It consists of two independent rounds:

1. The First round of the Olympiad will start on October 14, 2018 at 16:00 (UTC +7). It lasts 4.5 hours and includes several problems of varying difficulties. Participation is individual.
2. The Second round of the Olympiad will take place during one week, October 15 – October 22, 2018. It lasts for a whole week and in addition to normal problems includes open problems in cryptology, where you can try to submit an interesting partial result and get some points. Participation is in teams of up to 3 persons.

There are different sections — school students, university students and professionals.

I think everyone can find interesting problems and learn something new.

Enjoy!

Hello everyone!

Here's an interesting problem. Sounds easy at first but I could not find a solution that matches experimental results. Maybe I am missing some simple observation.

You are given two integers 1 ≤ l₁, l₂ ≤ 2ⁿ. Consider two random subsets of n-bit vectors of sizes l₁, l₂ respectively. Let

, where & is a bitwise AND.

Compute the expected size of R (in polynomial in n time). Computing maximum possible size of R is interesting too.

An easier version is when bitwise AND is replaced by bitwise XOR, it is also interesting.

NOTE: I am not sure that this problem has a solution.