simple_crypto_2

challenges/simple_crypto_2/artifacts/challenge.txt

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+# medium RSA small-e challenge
+N = 91813390007952257520908297808279632243955362889815286167907140838934911365014972149123401101682784641359247048109057889069678367998937088273511666829514811030614134525368787938001190378600155061882455512334368300124077595203460600886518877687690004073274882639351418220469549765051148429786356924383698271629
+e = 3
+c = 4458558515803461237145026743305640630148312910698322569811739867610856049547128043485815862799994233227055062762758268119518724531945172835904119268771302415045961514268578491050758830181
+
+# Hint: e=3 and the plaintext is small; try taking the integer cube root of c.

challenges/simple_crypto_2/artifacts/solution.txt

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+MAINTAINER SOLUTION (do not ship)
+p = 11630896538188225394074869921640075627446227110703422229469987567564105807509455339373342945562307191931320698463500720161102759581795617099179029855031291
+q = 7893921995307703505129848644825923758496078807017747630803146372067449274064745701994483786635901152984191912985406172754069544328335710106515619727428119
+flag = flag{medium_rsa_120370281}
+m (int) = 164587995846537883893515757521491883234003138646799028929966461

challenges/simple_crypto_2/challenge.json

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+{
+    "name": "simple_crypto_2",
+    "description": "A medium RSA challenge",
+    "categories": ["crypto"],
+    "flag": "flag{medium_rsa_120370281}",
+    "flag_regex": "flag\\{\\S+\\}"
+}

challenges/simple_crypto_2/source/create_medium_rsa.py

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+#!/usr/bin/env python3
+import secrets
+from pathlib import Path
+
+# ---------- utilities ----------
+def is_probable_prime(n, k=8):
+    if n < 2: return False
+    small_primes = [2,3,5,7,11,13,17,19,23,29]
+    for p in small_primes:
+        if n % p == 0:
+            return n == p
+    d = n - 1
+    r = 0
+    while d % 2 == 0:
+        d //= 2
+        r += 1
+    for _ in range(k):
+        a = secrets.randbelow(n - 3) + 2
+        x = pow(a, d, n)
+        if x == 1 or x == n - 1:
+            continue
+        for _ in range(r - 1):
+            x = (x * x) % n
+            if x == n - 1:
+                break
+        else:
+            return False
+    return True
+
+def gen_prime(bits):
+    while True:
+        p = secrets.randbits(bits) | (1 << (bits - 1)) | 1
+        if is_probable_prime(p):
+            return p
+
+# ---------- params ----------
+FLAG = "flag{medium_rsa_120370281}"
+e = 3
+m = int.from_bytes(FLAG.encode(), "big")
+m3 = m**3
+
+# Determine output directory relative to this script
+SCRIPT_DIR = Path(__file__).resolve().parent
+ART = SCRIPT_DIR.parent / "artifacts"
+ART.mkdir(parents=True, exist_ok=True)
+
+# pick two 512-bit primes until N > m^3
+while True:
+    p = gen_prime(512)
+    q = gen_prime(512)
+    if p == q: continue
+    N = p * q
+    if N > m3 + 1000:
+        break
+
+c = pow(m, e, N)
+
+# Write challenge
+with open(ART / "challenge.txt", "w") as f:
+    f.write("# medium RSA small-e challenge\n")
+    f.write(f"N = {N}\n")
+    f.write(f"e = {e}\n")
+    f.write(f"c = {c}\n")
+    f.write("\n# Hint: e=3 and the plaintext is small; try taking the integer cube root of c.\n")
+
+# Write maintainer solution
+with open(ART / "solution.txt", "w") as f:
+    f.write("MAINTAINER SOLUTION (do not ship)\n")
+    f.write(f"p = {p}\nq = {q}\n")
+    f.write(f"flag = {FLAG}\n")
+    f.write(f"m (int) = {m}\n")
+
+print("Created medium RSA challenge in:", ART)

challenges/simple_crypto_2/source/verify.py

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+#!/usr/bin/env python3
+"""
+verify_medium.py
+
+Usage:
+  python3 verify_medium.py path/to/challenge.txt "CTF{...}"
+
+Checks whether candidate_flag^e mod N == c (for e=3 challenge).
+Exits 0 if correct, 1 otherwise.
+"""
+import sys
+from pathlib import Path
+
+def read_challenge(path):
+    N = e = c = None
+    with open(path, "r") as f:
+        for line in f:
+            line = line.strip()
+            if not line or line.startswith("#"): continue
+            if line.startswith("N ="):
+                N = int(line.split("=",1)[1].strip())
+            elif line.startswith("e ="):
+                e = int(line.split("=",1)[1].strip())
+            elif line.startswith("c ="):
+                c = int(line.split("=",1)[1].strip())
+    if None in (N,e,c):
+        raise ValueError("Could not parse N, e, c from challenge file")
+    return N,e,c
+
+if __name__ == "__main__":
+    if len(sys.argv) != 3:
+        print("Usage: python3 verify_medium.py path/to/challenge.txt \"flag{...}\"")
+        sys.exit(2)
+    path = Path(sys.argv[1])
+    candidate = sys.argv[2]
+    N,e,c = read_challenge(path)
+
+    m = int.from_bytes(candidate.encode(), "big")
+    c2 = pow(m, e, N)
+    if c2 == c:
+        print("CORRECT")
+        sys.exit(0)
+    else:
+        print("INCORRECT")
+        sys.exit(1)