add: finally done with crypto/bcc

Cryptography/bcc/README.md

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+# BCC
+
+to-do

Cryptography/bcc/challenge.yml

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+name: "BCC"
+category: Cryptography
+description: |-
+  Beelliptic Curve Cryptography, or BCC, is a cryptographic scheme based on the mathematical properties of bees and elliptic curves. Buzzing with security, BCC offers a unique approach to encryption and digital signatures, making it a sweet choice for protecting sensitive information in the digital age. Your task is to exploit the weaknesses in the BCC implementation to retrieve the flag.
+
+  Author: ringoshiro
+
+##### DON'T CHANGE
+value: 500
+type: dynamic
+extra:
+    initial: 500
+    decay: 30
+    minimum: 100
+##### DON'T CHANGE
+
+flags:
+  - BEECTF{4uth0r_n33d5_r3st_n0w...}
+
+tags:
+  - medium
+
+files:
+  - dist/chall.py
+  - dist/output.txt
+
+state: hidden
+
+version: "0.1"

Cryptography/bcc/dist/chall.py

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+from secret import p, a, b, G, BETA
+
+def add(P, Q, a, p):
+    if P is None:
+        return Q
+    if Q is None:
+        return P
+    x1, y1 = P
+    x2, y2 = Q
+    if x1 == x2 and (y1 != y2 or y1 == 0):
+        return None
+    if x1 == x2:
+        m = (3 * x1 * x1 + a) * pow(2 * y1, -1, p) % p
+    else:
+        m = (y2 - y1) * pow(x2 - x1, -1, p) % p
+    x3 = (m * m - x1 - x2) % p
+    y3 = (m * (x1 - x3) - y1) % p
+    return (x3, y3)
+
+def mul(k, P, a, p):
+    R0 = None
+    R1 = P
+    for bit in bin(k)[2:]:
+        if bit == '0':
+            R1 = add(R0, R1, a, p)
+            R0 = add(R0, R0, a, p)
+        else:
+            R0 = add(R0, R1, a, p)
+            R1 = add(R1, R1, a, p)
+    return R0
+
+flag = int.from_bytes(b"BEECTF{xxxxxxxxxxxxxxxxxxxxxxxx}")
+kprime = (flag + BETA) % (p - 1)
+
+Gx = G[0]
+Qx = mul(kprime, G, a, p)[0]
+Rx = mul(BETA, G, a, p)[0]
+
+print(f'{p = }')
+print(f'{a = }')
+print(f'{Gx = }')
+print(f'{Qx = }')
+print(f'{Rx = }')

Cryptography/bcc/dist/output.txt

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+p = 3059506932006842768669313045979965122802573567548630439761719809964279577239571933
+a = 2448848303492708630919982332575904911263442803797664768836842024937962142592572096
+Gx = 1175626665511163128867519385055567089318632886502007689116591740322574196248254667
+Qx = 1692192797051786849921937448962108889305900850182074908387601492835973879030967392
+Rx = 432244659212727282574552361819256527291075425049776311256018620682846747709939971

Cryptography/bcc/src/flag.txt

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+BEECTF{4uth0r_n33d5_r3st_n0w...}