From d4b4d1df2e65bf3fb2d215459885e381e3518e50 Mon Sep 17 00:00:00 2001 From: Julien CLEMENT Date: Sat, 26 Mar 2022 11:32:54 +0100 Subject: [PATCH] fix(q-solved): add table of contents and typo fixes Signed-off-by: Julien CLEMENT --- jujure/content/writeups/q-solved.md | 35 ++++++++++++++++------------- 1 file changed, 20 insertions(+), 15 deletions(-) diff --git a/jujure/content/writeups/q-solved.md b/jujure/content/writeups/q-solved.md index ba4c037..6a97b8d 100644 --- a/jujure/content/writeups/q-solved.md +++ b/jujure/content/writeups/q-solved.md @@ -3,22 +3,27 @@ title: "Reversing quantum algorithms ~~for ctf points~~ | q-solved - zer0pts 202 date: "2022-03-25 18:00:00" author: "Juju" tags: ["Reverse", "Quantum", "Writeup", "zer0pts"] +toc: true --- -# Challenge description +# Intro + +## Challenge description `quantum` `reverse` | `304 pts` `8 solves` ``` I copied the solver of a reversing task from the future. But it doesn't show the flag forever :thinking: ``` -# Given files +## Given files {{< code file="/static/q-solved/solve.py" language="py" >}} [circuit.json](/q-solved/circuit.json) -# TL;DR +# Writeup + +## TL;DR The scripts builds a quantum circuit describing an unstructured search algorithm inspired by the grover's algorithm. Its goal is to find among all @@ -38,17 +43,17 @@ described by the oracle. All that remains to do for us is to understand what that criteria is. -# Reversing the Oracle +## Reversing the Oracle We can see that the oracle is built using the `circuit.json`. The oracle is composed of 1408 multi-controlled X (MCX) gates, each controlled by 1 -or 3 input qubits with with a control state given in the json. Each MCX gate +or 3 input qubits with a control state given in the json. Each MCX gate acts on a dedicated ancilla qubit. -After all 1408 MCX, the circuit adds an other MCX on the target qubit with all -control states set to 0. The target qubit is therefore introduced a phase shift -when all ancillas are in `|0>`. +After all 1408 MCX, the circuit adds an other MCX on the target qubit +controlled by all ancillas with all control states set to 0. The target qubit +is therefore introduced a phase shift when all ancillas are in `|0>`. So we want all ancillas to be `|0>` but it is also their original state. We therfore have to influence the control qubits of each MCX so that none actually @@ -66,7 +71,7 @@ the gate. Similarly, a qubit marked `True` must take value `|1>`. So we said earlier that the MCX have either 3 or 1 control bits and that at least 1 of the control qubits must mismatch from their control state. -# POC with trivial qubits +## POC with trivial qubits Obviously this results in an equation system but let's see what we get with only the obvious qubits: the ones controlling an ancilla by themselves. @@ -82,23 +87,23 @@ So let's try to set all obvious qubits: Well, most of them are 0, except, the first byte: `z` -Which is a really good sign that we are indead decoding a flag of the form +Which is a good sign that we are indeed decoding a flag of the form `zer0pts{...}` -# Equation system +## Equation system -For MCX with 3 control bits, we simply need to put them in an equation system, -with the trivial qubits. +For MCX with 3 control qubits, we simply need to put them in an equation +system alongside the trivial qubits. We will have a total of 1408 equations, 1 for each MCX, each equation basically -saying that at least 1 Qubit must be different from its control state, and +saying that at least 1 qubit must be different from its control state, and therefore equal to its assigned boolean in the json. Once the system is solved, we will know the state of all qubits that match the oracle, which is the one outputed by the quantum circuit. We will then be able to decode it to get the flag. -# Solve +## Solve I used z3 to build and solve the equation system: