Knowledge Base
Diffie-Hellman Parameter
A+

2048-bit Postfix 3.1 builtin DH parameter

Summary

Name:
2048-bit Postfix 3.1 builtin DH parameter
Key size:
2048 bits

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Security

A+
Key Size
Name

2048

Security

The Diffie-Hellman ephemeral public key parameter[409][410][411] with prime size greater than 2048[422] is considered secure, not weakened against logjam attack[7][8][9][10].

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-----
MIIBEwKCAQwwggEIAoIBAQC/KBtoaZAvN59aUCNzLBHyrHw+WLkjPgIHTbrZLMGe
+cQvvI2GSyqHhpMyD3JA/n6iwTLwZZzDGSUt62pJlHktob4FJqyNadwufrX9PCt9
QyJT9h4ERddThP1rEnJHBK+krEtVtnlCQIhUSNVNOrK/bCaVKd2Lnu24YI61NbYi
RB/7VnT+8CzmDCLJNbMblrsKWsMJoMylQJAPWaKJaSppeeTTJMaM2ryYOlsWrmNs
C0NP8y7IqWtYaqmOZAk9iERPlywdmLCpwLaNGTcft8mGqNw3TWQn8/Ure2t2hD/B
I5ctcfe2wjUoEJbWaQwuH5/fgoFXVzml8oEpV/kv0AOrAgECAgEC
-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----
MIIBFwKCAQwwggEIAoIBAQC/KBtoaZAvN59aUCNzLBHyrHw+WLkjPgIHTbrZLMGe
+cQvvI2GSyqHhpMyD3JA/n6iwTLwZZzDGSUt62pJlHktob4FJqyNadwufrX9PCt9
QyJT9h4ERddThP1rEnJHBK+krEtVtnlCQIhUSNVNOrK/bCaVKd2Lnu24YI61NbYi
RB/7VnT+8CzmDCLJNbMblrsKWsMJoMylQJAPWaKJaSppeeTTJMaM2ryYOlsWrmNs
C0NP8y7IqWtYaqmOZAk9iERPlywdmLCpwLaNGTcft8mGqNw3TWQn8/Ure2t2hD/B
I5ctcfe2wjUoEJbWaQwuH5/fgoFXVzml8oEpV/kv0AOrAgECAgECAgIA4Q==
-----END DH PARAMETERS-----
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PARI/GP

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

g = 0x2;
p = 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;
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

$\begin{eqnarray}
p \equiv 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 \\
g \equiv 0x2 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
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