Knowledge Base
Diffie-Hellman Parameter
A+

2048-bit ProFTPD 1.2.8 builtin DH parameter

Summary

Name:
2048-bit ProFTPD 1.2.8 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)
0x2
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Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----
MIIBCAKCAQEA0Ob/HzngzIWspObdBuUtv+pkLseZig/LPJ3urGH/aTFx/i97ZZWg
pFm442ZbP9hCmU8JRMWNi10WqgVuixFZH9cRhIdNvru6mvDD4g64D/0IsUiY3ona
ABUEpFG+W2AKDiCsxYNdxA+jjhFmLNNhXxaDqs9SnH116spno6tYn2cXoFQ6K8q1
A35QvZke77KPtPvSLWqposDU0mhsIXF4dYJM2OgsC8k/9vBk2W52y7uZ+7wVVHt/
lzaPCxz/3SiZ5TqtzYSroe+yIerWSSJqMGpjLlJ5z7zCti6lXbPawt0C6iYvOwoS
u6LvK/rMJWMbwwAYjza3MFpVGuASodKckwIBAg==
-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----
MIIBDAKCAQEA0Ob/HzngzIWspObdBuUtv+pkLseZig/LPJ3urGH/aTFx/i97ZZWg
pFm442ZbP9hCmU8JRMWNi10WqgVuixFZH9cRhIdNvru6mvDD4g64D/0IsUiY3ona
ABUEpFG+W2AKDiCsxYNdxA+jjhFmLNNhXxaDqs9SnH116spno6tYn2cXoFQ6K8q1
A35QvZke77KPtPvSLWqposDU0mhsIXF4dYJM2OgsC8k/9vBk2W52y7uZ+7wVVHt/
lzaPCxz/3SiZ5TqtzYSroe+yIerWSSJqMGpjLlJ5z7zCti6lXbPawt0C6iYvOwoS
u6LvK/rMJWMbwwAYjza3MFpVGuASodKckwIBAgICAOE=
-----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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