Knowledge Base
Diffie-Hellman Parameter
A+

2048-bit ProFTPD 1.3.8 builtin DH parameter

Summary

Name:
2048-bit ProFTPD 1.3.8 builtin DH parameter
Key size:
2048 bits
Publishers:

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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)
0x5
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Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----
MIIBCAKCAQEAokZl6gkqR508V6bb9q3ThOotaZe/XOwJ+Rsn+awFG7p6OIUzELov
Bu+fMafN6RBREAYCz4D8rTDMcKS6lSg/y2D58npjQ3drDrOUjuC63S4a9neCxb2c
1LRhSdcKcjm0mpvQBBcAUsDsk3iMKceJzPqR7/TJV0AKuigPfHBkh7fuB8Z0hNk2
dotwrzEPvA5NFKXnT38V5vPyAFmZOHsYVxcn1GcSL1ktNQ1I9ixh49dMW20vsAWn
fNvJMXEuBSWSKkAjgEjI/qL5Wzf7QmiT72ZcJgbVPSYdi4Tv5vh0LC5ArdubHkX/
CGtf9RcxDu8h52EK+qJp77xv6c+U4qDHiwIBBQ==
-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----
MIIBDAKCAQEAokZl6gkqR508V6bb9q3ThOotaZe/XOwJ+Rsn+awFG7p6OIUzELov
Bu+fMafN6RBREAYCz4D8rTDMcKS6lSg/y2D58npjQ3drDrOUjuC63S4a9neCxb2c
1LRhSdcKcjm0mpvQBBcAUsDsk3iMKceJzPqR7/TJV0AKuigPfHBkh7fuB8Z0hNk2
dotwrzEPvA5NFKXnT38V5vPyAFmZOHsYVxcn1GcSL1ktNQ1I9ixh49dMW20vsAWn
fNvJMXEuBSWSKkAjgEjI/qL5Wzf7QmiT72ZcJgbVPSYdi4Tv5vh0LC5ArdubHkX/
CGtf9RcxDu8h52EK+qJp77xv6c+U4qDHiwIBBQICAOE=
-----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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