Asymmetric Cryptography

Asymmetric crypto challenges usually revolve around math or implementation mistakes rather than brute-forcing keys. RSA, ECC, and Diffie-Hellman are the core families to understand first.

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Quick RSA Attack Selection

Given $n$, $e$, $c$:

• $e = 3$ and $m^3 < n$: cube-root / small exponent
• $n$ factorable: FactorDB, yafu, Fermat
• Very large $e$, small $d$: Wiener (or related)
• Same $m$, same $n$, $\gcd(e_1,e_2)=1$: common modulus
• Same $m$, $e = 3$, three coprime moduli: Håstad broadcast

Given $p$, $q$, $e$, $c$: compute $d \equiv e^{-1} \pmod{(p-1)(q-1)}$ (or $\lambda(n)$), then $m \equiv c^d \pmod{n}$.

Automate: python3 RsaCtfTool.py -n N -e E --uncipher C

Quick ECC Attack Selection

Use SageMath for all ECC math.

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Last updated on Aug 1, 2025