n-ari n-ari

Beginner's Misc

The problem is:

exploit = input('? ')
if eval(b64encode(exploit.encode('UTF-8'))) == math.pi:
  print(open('flag.txt').read())

Slowest Decryption

This is PPC problem.

For any i, v, x, we define cnt(i,v,x) as the number of P such that GCD(P)=v and P[i]=x. Then, the answer will be \sum_{i,v,x} cnt(i,v,x) * v * c[x] * i. Because cnt(i,v,x) = cnt(i',v,x), the answer can be written as \sum_{v,x} cnt(0,v,x) * v * c[x] * N*(N-1)/2.

To count cnt(0,v,x), we fix x. Then we check v from N-1 to 1 such that x % v = 0.

TSG CTF 2020 writeups (日本語簡略版)

Beginner's Crypto

flag * 2^{10000} mod 10^{175} == val という形で、val が分かっている。

剰余の定義から flag * 2^{10000} - k * 10^{175} == val がわかる。

Modulus Amittendus

You can see that n, e, cf are exported in pubkey.json.

These values are a bit strange:

  def initialize
    # ...
    @cf = modinv(@q, @p)   # (1)

Rubikrypto

This is only ElGamal cryptosystem on Rubik Cube.

The order of Rubik Cube Group is 43_252_003_274_489_856_000n and this is small enough to use Pohlig-Hellman.

So the algorithm is simple:

get g, h, c1, c2.
calculate y = log_g(c1) using Pohlig-Hellman.

Sweet Like Apple Pie

The output is output = sin(flag % pi()).

We can get flag % pi() = arcsin(output) using a binary search. Note that there are 2 possible answers.

So, we want to calculate k such that flag - k * pi() = arcsin(output).

Due to the Decimal, these values are calculated in 300-digits precision. That means,

Beginner's Crypto

Given val such that flag * 2^{10000} mod 10^{175} == val.

From definition of modulus, we get flag * 2^{10000} - k * 10^{175} == val.

Divide by 2^{175}, flag * 2^{10000-175} - k * 5^{175} == val / 2^{175}

	// main関数内以外は全てサンプルコードのままです

	#include <iostream>
	#include <vector>
	#include <string>
	#include <random>
	#include <thread>
	#include <chrono>
	using namespace std;

	#include <stdio.h>
	#include <algorithm>

	namespace sudoku {
	const char UNKNOWN = '_';
	char board[90];
	void input(){
	for(int row=0; row<9; row++){
	scanf("%s",board + 9*row);
	}

	/login.html /login.html 200!
	/* 200! Role=admin
	/* /login.html?redirect=/:splat 302!