Add stub of approximate-gcd-experiment

.github/workflows/check_scripts.yml

@@ -18,7 +18,7 @@ jobs:
       - name: Install dependencies
         run: |
           python -m pip install --upgrade pip
-          pip install pylint -r algorithm/smart-attack/requirements.txt
+          pip install pylint mypy -r algorithm/smart-attack/requirements.txt
 
       - name: Set up Go
         uses: actions/setup-go@v4
@@ -30,6 +30,8 @@ jobs:
           pylint algorithm/smart-attack/smart_attack.py --fail-under=9
           python algorithm/smart-attack/smart_attack.py test
           pylint algorithm/ecpp/binary_quad.py --fail-under=9
+          pylint algorithm/approximate-gcd-experiment/gen_rsa.py --fail-under=9
+          mypy algorithm/approximate-gcd-experiment/gen_rsa.py
 
       - name: Check scripts in general
         run: |

algorithm/approximate-gcd-experiment/README.md

@@ -0,0 +1,4 @@
+# Approximate GCD の実験
+CTF の問題 Sign (ISITDTU CTF QUALS 2024) についての解析。問題内容は https://docs.google.com/spreadsheets/d/1nmj0uAPWkWbC0uXBoA7eBef_a6cRJ-UgTDuuh0gAc2Y/edit?usp=sharing を見ること。
+
+解析した結果のスプレッドシートは https://docs.google.com/spreadsheets/d/1nmj0uAPWkWbC0uXBoA7eBef_a6cRJ-UgTDuuh0gAc2Y/edit?usp=sharing である。

algorithm/approximate-gcd-experiment/approx_gcd.sage

@@ -0,0 +1,16 @@
+def approx_gcd(d: list[int], approx_error: int) -> int:
+    """
+    Returns q where d[0] ~= qx and d[i]'s are close to multiples of x.
+    The caller must find (d[0] + q // 2) // q if they want to find x.
+    """
+    l = len(d)
+    M = Matrix(ZZ, l, l)
+    M[0, 0] = approx_error
+    for i in range(1, l):
+        M[0, i] = d[i]
+        M[i, i] = -d[0]
+    L = M.LLL()
+    for row in L:
+        if row[0] != 0:
+            quot = abs(row[0] // approx_error)
+            return quot