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6144
The Diffie-Hellman ephemeral public key parameter[409][410][411] with a prime size greater than 4096[590] is considered secure but weakened against the D(HE)at attack[581][582][583][584], which is a denial-of-service attack[585][586][587][588][589] against the Ephemeral Diffie-Hellman[405][406][407][408] key exchange[133].
Use a well-known Diffie-Hellman ephemeral public key parameter[426][427][428], or generate a custom Diffie-Hellman ephemeral public key parameter[409][410][411] with a size greater or equal than 2048 bits but less or equal than 4096 bits. In the case of custom parameters, validate that the prime is a safe prime[176] to avoid a small subgroup confinement attack[72][73].
False
The Diffie-Hellman[99][100][101][102][103] key exchange provides no protection against a cryptanalytic attack by a quantum computer, and no classical Diffie-Hellman does — just as no classical elliptic curve does — because a quantum computer breaks the hardness assumption they rely on. Only a hybrid key exchange (a classical algorithm combined with a post-quantum cryptography[158][159] one) or a pure post-quantum algorithm is quantum-safe.
Enable a hybrid key exchange or a pure post-quantum algorithm on your server, and prefer it where the configuration allows, so the connection stays secure against a future quantum computer.
-----BEGIN DH PARAMETERS----- MIIDCAKCAwEA//////////+t+FRYortKmq/cViAnPTzx2LnFg84tNpWp4TZBFGQz +8yTnc4kmz75fS/jY2MMddj2gbICrsRhetPfHtXV/WVhJDP1H18GbtCFY2VVPe0a 87VXE15/V8k1mE8McODmi3fipona8+/och3xWKE2rec1MKzKT0g6eXq8CrGCsyT7 YdEIqUuyyOP7uWrat2DX9GgdT0Kj3jlN9K5W7edjcrsZCwenyO4KbXCeAvzhzffi 7MA0BM0oNC9hkXL+nOmFg/+OTxIy7vKBg8P+OxtMb61zO7X8vC7CIAXFjvGDfRaD ssbzSibBsu/6iGtCOGEfz9zeNVs7ZRkDW7w09N75nAI4YbRvydbmyQd62R0mkff3 7lmMsPrBhtkcrv4TCYUTknC0EwyTvEN5RPT9RFLi103TZPLiHnH1S/9croKrnJ32 nuhtK8UiNjoNq8Uhl5sN6todv5pC1cRITgq80Gv6U93vPBsg7j/VnXwl5B0rZp4e 8W5vUsMWTfT7eTDp5OWIV7asfV9C1p9tGHdjzx1VA0AEh/VbpX4xzHpxNciG77Qx iu1qHgEtnmgyqQdgCpGBMMRtx3j5ca0AOAkpmaMzy4t6Gh25PXFAADwqTs6p+Y0K zAqCkc3OyX3Pjsm1Wn+IpGtNtahR9EGC4caKAH5eDdkCC/1ktkUDbHpOZ30sOFMq OiO6RELK9T6mO7RUMpt2JMiRe91kscD9TLOOjDNMcBw6za0GV/zP7HGbH1w+TkYE HziBR/tM/bR3pSRx96mpaRC4VTIu22NA2KAO8JI1BRHjCr7B//njom5/sp+MGDAj w1h+ONoAd9m0dj5OS5Syu8GUxmUed8r5ku6qwCMqKBv2s6c5wSJhFoIK6NtYR6Z8 vvnJCRtGLVOM1ysDdGrnf15iKSwxFWKoRlBdyC24VDOK5J9SNclbkReMzy3Vys70 A+ydGBDGJysEWztx+dxrgNY/3UqOmtseaWKmlSbUMWHBpB1XDXk42tSkDjKc0OQO Zf//////////AgEC -----END DH PARAMETERS-----
-----BEGIN DH PARAMETERS----- MIIDDAKCAwEA//////////+t+FRYortKmq/cViAnPTzx2LnFg84tNpWp4TZBFGQz +8yTnc4kmz75fS/jY2MMddj2gbICrsRhetPfHtXV/WVhJDP1H18GbtCFY2VVPe0a 87VXE15/V8k1mE8McODmi3fipona8+/och3xWKE2rec1MKzKT0g6eXq8CrGCsyT7 YdEIqUuyyOP7uWrat2DX9GgdT0Kj3jlN9K5W7edjcrsZCwenyO4KbXCeAvzhzffi 7MA0BM0oNC9hkXL+nOmFg/+OTxIy7vKBg8P+OxtMb61zO7X8vC7CIAXFjvGDfRaD ssbzSibBsu/6iGtCOGEfz9zeNVs7ZRkDW7w09N75nAI4YbRvydbmyQd62R0mkff3 7lmMsPrBhtkcrv4TCYUTknC0EwyTvEN5RPT9RFLi103TZPLiHnH1S/9croKrnJ32 nuhtK8UiNjoNq8Uhl5sN6todv5pC1cRITgq80Gv6U93vPBsg7j/VnXwl5B0rZp4e 8W5vUsMWTfT7eTDp5OWIV7asfV9C1p9tGHdjzx1VA0AEh/VbpX4xzHpxNciG77Qx iu1qHgEtnmgyqQdgCpGBMMRtx3j5ca0AOAkpmaMzy4t6Gh25PXFAADwqTs6p+Y0K zAqCkc3OyX3Pjsm1Wn+IpGtNtahR9EGC4caKAH5eDdkCC/1ktkUDbHpOZ30sOFMq OiO6RELK9T6mO7RUMpt2JMiRe91kscD9TLOOjDNMcBw6za0GV/zP7HGbH1w+TkYE HziBR/tM/bR3pSRx96mpaRC4VTIu22NA2KAO8JI1BRHjCr7B//njom5/sp+MGDAj w1h+ONoAd9m0dj5OS5Syu8GUxmUed8r5ku6qwCMqKBv2s6c5wSJhFoIK6NtYR6Z8 vvnJCRtGLVOM1ysDdGrnf15iKSwxFWKoRlBdyC24VDOK5J9SNclbkReMzy3Vys70 A+ydGBDGJysEWztx+dxrgNY/3UqOmtseaWKmlSbUMWHBpB1XDXk42tSkDjKc0OQO Zf//////////AgECAgIBdw== -----END DH PARAMETERS-----
powermod(x, k, m) = lift(Mod(x, m) ^ k); g = 0x2; p = 2^6144 - 2^6080 + (floor(2^6014 * exp(1)) + 15705020) * 2^64 - 1; s = 256; a = 2 ^ (s - 1) + random(2 ^ (s - 1)); A = powermod(g, a, p); b = 2 ^ (s - 1) + random(2 ^ (s - 1)); B = powermod(g, b, p); S = powermod(B, a, p);
$\begin{eqnarray}
p \equiv 2^{6144} - 2^{6080} + (\lfloor 2^{6014} * e \rfloor + 15705020) * 2^{64} - 1 \\
g \equiv 0x2 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$