Knowledge Base
Diffie-Hellman Parameter
A+

3072-bit ProFTPD 1.3.8 builtin DH parameter

Summary

Name:
3072-bit ProFTPD 1.3.8 builtin DH parameter
Key size:
3072 bits
Publishers:

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Security

A+
Key Size
Name

3072

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)
0xc1d87c6c1067e0fcb4173725888272f83ecc597b50d742ce0a29111d076d81007845b8706f88671f24f4df7b72b48542fa05de1ce9df7a6f72d223960eb1e90f58bf5696b1f222b39ce0aafc75f5d58c5422c33be161b76f4719c537f2051019803490d7be8d32d69b27634504f4c4a64e0d520cb5d6092a7fc17142be59a4aecbde2d28ce0612094059c31afb7187a9fe743b548ec636fb677bb05cd5347fe14fe161eab1993ff18bf44a9d6dcd164b58ae2ca1d7985072d788240c8419016f1556fd0575b72ea8caa96b360ba1dc88dd47cfa719b4db9ad7d0f43c458224e90f7da301f383b32f6cf0e465757d7b81416273032b28de0ca90fa35270cb19605b499df0e52d1c16b8a7111dccd14ce95a555a533035065873735a0acaa846f27ac36b107ed4ef9335b44ee5c32a93c4c6e2237d291006974c0f1ba043bff90c25816ec80708ee286183103ac32db8ced2452a31ccbfcbb6d63a71fcdde7473ab95cf781c10d2503f859049288aa809ce332792641e9c144e6f6bf59e6151e53
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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 = 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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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