calculus

official/超基础的数理模拟器/README.md

@@ -1 +1,54 @@
 # 超基础的数理模拟器
+
+这是一道简单的检查数理基础扎实与否的题目，网站会随机生成定积分的式子供选手计算，如果能答对 400 题即可拿到 flag。
+
+对于数理基础扎实的同学，你们通过口算定积分可以很轻松拿到 flag。
+
+但是，如果你们的数理基础不够扎实，有毅力的同学也可以将每一道题都输入 CASIO 计算器，重复 400 遍即可达成条件。
+
+对于没有 CASIO 计算器以及 Mathematica 等计算软件的同学，你们可以使用中国科技大学大雾实验专用坐标纸，在上面精准描绘之后数格点个数，不过由于本题精度要求较高，所以可能比较废纸。
+
+对于那些数理基础太不扎实的计院同学，你们可以考虑写出数理基础足够扎实的 python 代码，代替你们进行测试：
+
+```python
+# pip3 install sympy antlr4-python3-runtime
+import requests
+from sympy import Integral, Symbol, E, latex
+from sympy.parsing.latex import parse_latex
+from urllib.parse import quote_plus
+# from IPython.core.display import display, HTML
+
+e = Symbol('e')
+x = Symbol('x')
+
+token = 'REDACTED' # Use your own token here
+s = requests.session()
+s.get(f'http://202.38.93.111:10190/login?token={quote_plus(token)}')
+t = s.get('http://202.38.93.111:10190/').text
+num = 400
+
+while num > 1:
+    num = t[t.find('<h1 class="cover-heading">')+26:t.find('</h1>')]
+    num = int(num.split(' ')[1])
+    print(num)
+    m = t[t.find('<p> $')+5:t.find('{d x}$</p>')]
+
+    # display(HTML(f"${m}$"))
+
+    lu = m.split(' ')[0]
+    lower = lu[6:lu.find('^')-1]
+    lower = parse_latex(lower).n(20)
+    upper = lu[lu.find('^')+2:-1]
+    upper = parse_latex(upper).n(20)
+
+    m = ' '.join(m.split(' ')[1:])
+    m = m.replace(r'\right)', ')').replace(r'\left(', '(').replace(r'\,', '')
+    m = parse_latex(m).subs(e,E)
+
+    # display(HTML(f"${latex(m)}$"))
+
+    ans = Integral(m, (x, lower, upper)).n(10)
+    t = s.post('http://202.38.93.111:10190/submit', data={'ans':str(ans)}).text
+
+print(t)
+```

official/超基础的数理模拟器/src/docker-compose.yml

@@ -0,0 +1,13 @@
+version: "2.4"
+services:
+  simulator:
+    restart: always
+    build: simulator
+    ports:
+      - "10190:80"
+  generator:
+    restart: always
+    build: generator
+    scale: 8
+    expose:
+      - "5000"

official/超基础的数理模拟器/src/generator/Dockerfile

@@ -0,0 +1,11 @@
+FROM sagemath/sagemath
+
+RUN sudo sed -i 's/archive.ubuntu.com/mirrors.bfsu.edu.cn/g' /etc/apt/sources.list
+RUN sage -pip config set global.index-url https://pypi.tuna.tsinghua.edu.cn/simple
+RUN sage -pip install flask
+
+ADD gen.sage /home/sage
+
+EXPOSE 5000
+
+ENTRYPOINT sage gen.sage

official/超基础的数理模拟器/src/generator/gen.sage

@@ -0,0 +1,52 @@
+from flask import Flask
+from flask import request
+app = Flask(__name__)
+
+x = var('x')
+y = var('y')
+
+half1 = [log(x), sqrt(x)] # x >= 1
+half2 = [x/y, y/x] # y > 0 and y is int and x >= 1
+full1 = [e^x, sin(x), cos(x), sinh(x), cosh(x), arctan(x)]
+full2 = [x+y, x+y, x*y, x-y]
+
+def gen_f(depth=0):
+    if (randint(0,2) != 0 and depth < 4) or depth < 2:
+        return choice(full2)(x=gen_f(depth+1),y=gen_f(depth+1))
+    elif (randint(0,2) != 0 and depth < 4):
+        return choice(full1)(x=gen_f(depth+1))
+    elif randint(0,2) != 0:
+        return choice(half1)
+    else:
+        return choice(half2)(y=randint(1,4))
+
+def gen_q():
+    while True:
+        f = gen_f()
+        if f(x=1) == f(x=2) and f(x=2) == f(x=3):
+            continue
+        l = [QQ(randint(1,10))/QQ(randint(1,5)), QQ(randint(1,10))/QQ(randint(1,5))]
+        if l[0] == l[1]:
+            continue
+        l.sort()
+        fint = f.integral(x,l[0],l[1],hold=True)
+        result, eps = numerical_integral(f,l[0],l[1])
+        if abs(result) < 100000 and eps < 1e-7:
+            break
+
+    return (result, latex(fint).replace('log', 'ln'))
+
+@app.route('/')
+def gen():
+    try:
+        times = int(request.args.get('times'))
+    except:
+        times = 1
+    ret = ''
+    for i in range(times):
+        r, s = gen_q()
+        ret += str(r) + '\n' + s + '\n'
+    return ret
+
+if __name__ == '__main__':
+    app.run(host='0.0.0.0')

official/超基础的数理模拟器/src/simulator/Dockerfile

@@ -0,0 +1,6 @@
+FROM tiangolo/uwsgi-nginx-flask:python3.8
+
+COPY ./app /app
+
+RUN pip3 config set global.index-url https://pypi.tuna.tsinghua.edu.cn/simple
+RUN pip3 install requests pycryptodome pyopenssl

official/超基础的数理模拟器/src/simulator/app/cert.pem

@@ -0,0 +1,17 @@
+-----BEGIN CERTIFICATE-----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+-----END CERTIFICATE-----

official/超基础的数理模拟器/src/simulator/app/encrypted_session.py

@@ -0,0 +1,155 @@
+from werkzeug.datastructures import CallbackDict
+from flask.sessions import SessionInterface, SessionMixin
+
+from Crypto.Cipher import AES
+import json
+from json import JSONEncoder, JSONDecoder
+import base64
+import hashlib
+import zlib
+
+class EncryptedSession(CallbackDict, SessionMixin):
+
+    def __init__(self, initial=None):
+        def on_update(self):
+            self.modified = True
+        CallbackDict.__init__(self, initial, on_update)
+        self.modified = False
+
+
+class EncryptedSessionInterface(SessionInterface):
+    session_class = EncryptedSession
+    compress_threshold = 1024
+
+    def open_session(self, app, request):
+        '''
+        @param py: Flask py
+        @param request: Flask HTTP Request
+        @summary: Sets the current session from the request's session cooke. This overrides the default
+        Flask implementation, adding AES decryption of the client-side session cookie.
+        '''
+
+        # Get the session cookie
+        session_cookie = request.cookies.get(app.session_cookie_name)
+        if not session_cookie:
+            return self.session_class()
+
+        # Get the crypto key
+        crypto_key = app.config['SESSION_CRYPTO_KEY'] if 'SESSION_CRYPTO_KEY' in app.config else app.crypto_key
+        crypto_key = hashlib.sha256(crypto_key).digest()[:16]
+
+        # Split the session cookie : <z|u>.<base64 cipher text>.<base64 mac>.<base64 nonce>
+        itup = session_cookie.split(".")
+        if (len (itup) is not 4):
+            return self.session_class()     # Session cookie not in the right format
+
+        try:
+
+            # Compressed data?
+            if (itup[0] == 'z'):            # session cookie for compressed data starts with "z."
+                is_compressed = True
+            else:
+                is_compressed = False
+
+            # Decode the cookie parts from base64
+            ciphertext = base64.b64decode (bytes(itup[1], 'utf-8'))
+            mac = base64.b64decode (bytes(itup[2], 'utf-8'))
+            nonce = base64.b64decode (bytes(itup[3], 'utf-8'))
+
+            # Decrypt
+            cipher = AES.new (crypto_key, AES.MODE_EAX, nonce)
+            data = cipher.decrypt_and_verify (ciphertext, mac)
+
+            # Convert back to a dict and pass that onto the session
+            if is_compressed:
+                data = zlib.decompress (data)
+            session_dict = json.loads (str (data, 'utf-8'), cls=BinaryAwareJSONDecoder)
+
+            return self.session_class (session_dict)
+
+        except ValueError:
+            return self.session_class()
+
+    def save_session(self, app, session, response):
+        '''
+        @param py: Flask py
+        @param session: Flask / Werkzeug Session
+        @param response: Flask HTTP Response
+        @summary: Saves the current session. This overrides the default Flask implementation, adding
+        AES encryption of the client-side session cookie.
+        '''
+
+        domain = self.get_cookie_domain(app)
+        if not session:
+            if session.modified:
+                response.delete_cookie (app.session_cookie_name, domain=domain)
+            return
+        expires = self.get_expiration_time(app, session)
+
+        # Decide whether to compress
+        bdict = bytes (json.dumps (dict (session), cls=BinaryAwareJSONEncoder), 'utf-8')
+        if (len (bdict) > self.compress_threshold):
+            prefix = "z"                                    # session cookie for compressed data starts with "z."
+            bdict = zlib.compress (bdict)
+        else:
+            prefix = "u"                                    # session cookie for uncompressed data starts with "u."
+
+        # Get the crypto key
+        crypto_key = app.config['SESSION_CRYPTO_KEY'] if 'SESSION_CRYPTO_KEY' in app.config else app.crypto_key
+        crypto_key = hashlib.sha256(crypto_key).digest()[:16]
+
+        # Encrypt using AES in EAX mode
+        cipher = AES.new (crypto_key, AES.MODE_EAX)
+        ciphertext, mac = cipher.encrypt_and_digest (bdict)
+        nonce = cipher.nonce
+
+        # Convert the ciphertext, mac, and nonce to base64
+        b64_ciphertext = base64.b64encode (ciphertext)
+        b64_mac = base64.b64encode (mac)
+        b64_nonce = base64.b64encode (nonce)
+
+        # Create the session cookie as <u|z>.<base64 cipher text>.<base64 mac>.<base64 nonce>
+        tup = [prefix, b64_ciphertext.decode(), b64_mac.decode(), b64_nonce.decode()]
+        session_cookie = ".".join(tup)
+
+        # Set the session cookie
+        response.set_cookie(app.session_cookie_name, session_cookie,
+                            expires=expires, httponly=True,
+                            domain=domain)
+
+
+class BinaryAwareJSONEncoder(JSONEncoder):
+    """
+    Converts a python object, where binary data is converted into an object
+    that can be decoded using the BinaryAwareJSONDecoder.
+    """
+    def default(self, obj):
+        if isinstance(obj, bytes):
+            return {
+                '__type__' : 'bytes',
+                'b' : base64.b64encode (obj).decode ()
+            }
+
+        else:
+            return JSONEncoder.default(self, obj)
+
+class BinaryAwareJSONDecoder(JSONDecoder):
+    """
+    Converts a json string, where binary data was converted into objects form
+    using the BinaryAwareJSONEncoder, back into a python object.
+    """
+
+    def __init__(self):
+            JSONDecoder.__init__(self, object_hook=self.dict_to_object)
+
+    def dict_to_object(self, d):
+        if '__type__' not in d:
+            return d
+
+        typ = d.pop('__type__')
+        if typ == 'bytes':
+            return base64.b64decode (bytes (d['b'], 'utf-8'))
+        else:
+            # Oops... better put this back together.
+            d['__type__'] = typ
+            return d

official/超基础的数理模拟器/src/simulator/app/main.py

@@ -0,0 +1,87 @@
+import random
+import os
+import requests
+import time
+
+import OpenSSL
+import base64
+import hashlib
+
+from functools import wraps
+
+from flask import Flask, request, session, redirect, url_for, render_template, make_response
+from encrypted_session import EncryptedSessionInterface
+
+app = Flask(__name__, static_folder='static', static_url_path='', template_folder='templates')
+app.secret_key = b"REDACTED"
+app.config['SESSION_CRYPTO_KEY'] = b"REDACTED"
+app.session_interface = EncryptedSessionInterface()
+
+with open("cert.pem") as f:
+    cert = OpenSSL.crypto.load_certificate(OpenSSL.crypto.FILETYPE_PEM, f.read())
+
+def login_required(f):
+    @wraps(f)
+    def decorated_function(*args, **kwargs):
+        if 'token' not in session:
+            return redirect(url_for('login'))
+        return f(*args, **kwargs)
+    return decorated_function
+
+@app.route('/login')
+def login():
+    try:
+        token = request.args.get('token')
+        id, sig = token.split(":", 1)
+        sig = base64.b64decode(sig, validate=True)
+        OpenSSL.crypto.verify(cert, sig, id.encode(), "sha256")
+        session['token'] = token
+        session['score'] = 0
+        session.pop('ans', None)
+        return redirect(url_for('index'))
+    except Exception:
+        return make_response('''
+        您尚未登录或登录 token 错误, 请使用 hackergame 网站上的题目链接访问
+    ''', 403)
+
+@app.route('/logout')
+def logout():
+    session.pop('token', None)
+    session.pop('score', None)
+    session.pop('ans', None)
+    return redirect(url_for('login'))
+
+@app.route('/')
+@login_required
+def index():
+    total = 400
+    width = (session['score'] / float(total)) * 100
+    if width >= 100:
+        token = session['token']
+        return f"flag{{S0lid_M4th_Phy_Foundation_{hashlib.sha256(('S01idF'+token).encode()).hexdigest()[:10]}}}"
+    formula = requests.get("http://generator:5000").text.split('\n')
+    session['ans'] = float(formula[0])
+    #print(formula[0])
+    result = session.pop('result', None)
+    return make_response(render_template("index.html", remaining=total-session['score'], width=width, latex=formula[1], result=result))
+
+
+@app.route('/submit', methods=['POST'])
+@login_required
+def submit():
+    try:
+        ans = request.form['ans']
+        ans = float(ans)
+        if abs(session['ans'] - ans) < 1e-6:
+            session['score'] += 1
+            session['result'] = "true"
+        else:
+            session['result'] = "false"
+    except:
+        pass
+    session.pop('ans', None)
+    return redirect(url_for('index'))
+
+
+if __name__ == '__main__':
+    app.run(host='0.0.0.0', port=5001)

official/超基础的数理模拟器/src/simulator/app/templates/index.html

@@ -0,0 +1,100 @@
+<!DOCTYPE html>
+<html>
+
+<head>
+    <meta charset="UTF-8">
+    <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+    <link rel="shortcut icon" href="static/favicon.ico" />
+    <title>超基础的数理模拟器</title>
+
+    <link rel="stylesheet" href="static/bootstrap.min.css">
+    <link rel="stylesheet" href="static/font-awesome.min.css">
+
+    <script>window.console = window.console || function (t) { };</script>
+    <script>if (document.location.search.match(/type=embed/gi)) { window.parent.postMessage("resize", "*"); }</script>
+    <script>
+        MathJax = {
+            tex: {
+                inlineMath: [['$', '$'], ['\\(', '\\)']]
+            },
+            svg: {
+                fontCache: 'global',
+                scale: 1.2
+            }
+        };
+    </script>
+    <script type="text/javascript" id="MathJax-script" src="static/tex-svg.js">
+    </script>
+</head>
+
+<body translate="no">
+    <div class="container-fluid">
+        <div class="row">
+            <div class="col-md-12">
+                <nav class="navbar navbar-expand-lg navbar-light bg-light navbar-dark bg-dark">
+
+                    <button class="navbar-toggler" type="button" data-toggle="collapse"
+                        data-target="#bs-example-navbar-collapse-1">
+                        <span class="navbar-toggler-icon"></span>
+                    </button> <a class="navbar-brand" href="#">超基础的数理模拟器</a>
+                    <div class="collapse navbar-collapse" id="bs-example-navbar-collapse-1">
+                        <ul class="navbar-nav ml-md-auto">
+                            <a href="logout" class="btn btn-primary my-2 my-sm-0">
+                                溜了溜了
+                            </a>
+                        </ul>
+                    </div>
+                </nav>
+                <div class="progress">
+                    <div class="progress-bar progress-bar-striped  progress-bar-animated bg-success" role="progressbar"
+                        style="width: {{ width }}%" aria-valuemin="0" aria-valuemax="100"></div>
+                </div>
+                {% if result == 'true' %}
+                <div class="alert alert-success" role="alert">
+                    答案正确! 小小年纪, 果然满脑子都是<b>数理基础</b>呢
+                </div>
+                {% endif %}
+                {% if result == 'false' %}
+                <div class="alert alert-danger" role="alert">
+                    答案错误 /(ㄒoㄒ)/~~ 又是数理基础不扎实的一天
+                </div>
+                {% endif %}
+                <div class="row" style="margin-top:5px">
+                    <div class="col-md-4">
+                    </div>
+                    <div class="col-md-4 alert alert-info text-center">
+                        <p class="lead" style="margin-bottom:5px">继续答对</p>
+                        <h1 class="cover-heading"> {{ remaining }} 题</h1>
+                        <p class="lead" style="margin-bottom:5px">即可视为通过(数理基础扎实的)图灵测试</p>
+                    </div>
+                    <div class="col-md-4">
+                    </div>
+                </div>
+                <center>
+                    <p> ${{ latex }}$</p>
+                </center>
+                <div class="row">
+                    <div class="col-md-4">
+                    </div>
+                    <div class="col-md-4">
+                        <form action="/submit" method="POST">
+                            <div class="input-group">
+                                <input type="text" placeholder="请计算以上定积分的结果 (精确到小数点后六位)" class="form-control"
+                                    name="ans">
+                                <div class="pull-right" style="margin-left:5px">
+                                    <span class="input-group-btn">
+                                        <button class="btn btn-primary" type="submit">检查基础</button>
+                                    </span>
+                                </div>
+                            </div>
+                        </form>
+                    </div>
+                    <div class="col-md-4">
+                    </div>
+                </div>
+            </div>
+        </div>
+    </div>
+</body>
+
+</html>