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512
The Diffie-Hellman ephemeral public key parameter[409][410][411] with prime size less or equal than 768-bit[425] is weakened against logjam attack[7][8][9][10], but can only be exploited by an academic team.
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.
powermod(x, k, m) = lift(Mod(x, m) ^ k); g = 0x5; p = 0xfe727dbef4716cc2443a9c3244fbe7eb2c6c5f20235aadfcd7b65abf2b875ba76aea4801082f613372c2995acaa3399d62c5ccaad139917edf4502452e598c47; 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);
$\begin{eqnarray}
p \equiv 0xfe727dbef4716cc2443a9c3244fbe7eb2c6c5f20235aadfcd7b65abf2b875ba76aea4801082f613372c2995acaa3399d62c5ccaad139917edf4502452e598c47 \\
g \equiv 0x5 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$