Knowledge Base
Diffie-Hellman Parameter
A+

2048-bit ProFTPD 1.3.5 builtin DH parameter

Summary

Name:
2048-bit ProFTPD 1.3.5 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-----
MIIBCAKCAQEA8uoKASu5Z9sdFVdEvpQOhZvbpHT7a+ZEKrUu+FRnA9vzK3uGn6gk
GwrLE/wcWcxcLO56mAY91kiordKHZYTW8KYq6416bA3JrOtBwiZveSAXG6pa+SSk
g3Dn6iK2rMado8s2y1MTUYQDQ8LsqnYOrHv551fP0kMq7v9bV0rr90bF54P54RFd
VKMx82r76n5gEtsVNsVKbTabob3wZVjdCCIlSVpumGYWJXbu2zFPF03taSP8zDGr
Z9jCVY+cEoU4z1hrWgHTtovfhoW8i1ULNrGfOOcdMzGhK/VtuIU6RMKqfC6OhmZL
Md/fa3Ip5joGRWGnl2oEQEK29ARJxG7UAwIBBQ==
-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----
MIIBDAKCAQEA8uoKASu5Z9sdFVdEvpQOhZvbpHT7a+ZEKrUu+FRnA9vzK3uGn6gk
GwrLE/wcWcxcLO56mAY91kiordKHZYTW8KYq6416bA3JrOtBwiZveSAXG6pa+SSk
g3Dn6iK2rMado8s2y1MTUYQDQ8LsqnYOrHv551fP0kMq7v9bV0rr90bF54P54RFd
VKMx82r76n5gEtsVNsVKbTabob3wZVjdCCIlSVpumGYWJXbu2zFPF03taSP8zDGr
Z9jCVY+cEoU4z1hrWgHTtovfhoW8i1ULNrGfOOcdMzGhK/VtuIU6RMKqfC6OhmZL
Md/fa3Ip5joGRWGnl2oEQEK29ARJxG7UAwIBBQICAOE=
-----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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