Knowledge Base
Diffie-Hellman Parameter
D

8192-bit Finite Field Diffie-Hellman group (RFC 7919)

Summary

Name:
8192-bit Finite Field Diffie-Hellman group (RFC 7919)
Key size:
8192 bits
Publishers:

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Security

D
Key Size
Name

8192

Security

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].

Recommendations

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].

A+
Prime
Name

Safe Prime

Security

Diffie-Hellman ephemeral public key parameter[409][410][411] contains a safe prime[176], so the connection is certainly not vulnerable to a small subgroup confinement attack[72][73].

A
Post-Quantum
Name

False

Security

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.

Recommendations

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.

Parameter Numbers

Prime (p)
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Generator (g)
0x2
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Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----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-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----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-----END DH PARAMETERS-----
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PARI/GP

powermod(x, k, m) = lift(Mod(x, m) ^ k);

g = 0x2;
p = 2^8192 - 2^8128 + (floor(2^8062 * exp(1)) + 10965728) * 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);
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LaTeX

$\begin{eqnarray}
p \equiv 2^{8192} - 2^{8128} + (\lfloor 2^{8062} * e \rfloor + 10965728) * 2^{64} - 1 \\
g \equiv 0x2 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
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