Knowledge Base
Diffie-Hellman Parameter
A+

4096-bit ProFTPD 1.3.8 builtin DH parameter

Summary

Name:
4096-bit ProFTPD 1.3.8 builtin DH parameter
Key size:
4096 bits
Publishers:

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Security

A+
Key Size
Name

4096

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)
0x5
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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 = 0x5;
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

$\begin{eqnarray}
p \equiv 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 \\
g \equiv 0x5 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
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