Knowledge Base
Diffie-Hellman Parameter
A-

1536-bit ProFTPD 1.3.5 builtin DH parameter

Summary

Name:
1536-bit ProFTPD 1.3.5 builtin DH parameter
Key size:
1536 bits
Publishers:

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Security

A-
Key Size
Name

1536

Security

The Diffie-Hellman ephemeral public key parameter[409][410][411] with prime size less or equal than 2048-bit[423] might be weakened against logjam attack[7][8][9][10], however it will only be able to exploited by a national states.

Recommendations

Generate custom Diffie-Hellman ephemeral public key parameter[409][410][411] with size greater or equal than 2048 bits and validate that the prime in parameter is safe prime[176] or use a well-known Diffie-Hellman ephemeral public key parameter[426][427][428] with size greater or equal than 2048 bits.

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)
0x94ab27ae97f47a42451512b8e0d12219100858896cdb61459725aad551a89c4853aae9224443d4bfc094f9636b79923625709f7ee83873f996e8e9edeea62e40a3fb5412b92b5980383830c1592b4bc4ca77825596bfe07ccdb4267c99d4dc054fc754e864905724241cd7e8b5537750c3acd3af76ee63fb329b3258339b3fbf6111e53e5115af349c269dc233a60bc476d36b43572239731d68d012d330e940ecac324b0e753c74c6cc490a2b4d3a4163f3bf79e5de034e71e5c5c0b6934e33
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Generator (g)
0x5
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Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----
MIHHAoHBAJSrJ66X9HpCRRUSuODRIhkQCFiJbNthRZclqtVRqJxIU6rpIkRD1L/A
lPlja3mSNiVwn37oOHP5lujp7e6mLkCj+1QSuStZgDg4MMFZK0vEyneCVZa/4HzN
tCZ8mdTcBU/HVOhkkFckJBzX6LVTd1DDrNOvdu5j+zKbMlgzmz+/YRHlPlEVrzSc
Jp3CM6YLxHbTa0NXIjlzHWjQEtMw6UDsrDJLDnU8dMbMSQorTTpBY/O/eeXeA05x
5cXAtpNOMwIBBQ==
-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----
MIHLAoHBAJSrJ66X9HpCRRUSuODRIhkQCFiJbNthRZclqtVRqJxIU6rpIkRD1L/A
lPlja3mSNiVwn37oOHP5lujp7e6mLkCj+1QSuStZgDg4MMFZK0vEyneCVZa/4HzN
tCZ8mdTcBU/HVOhkkFckJBzX6LVTd1DDrNOvdu5j+zKbMlgzmz+/YRHlPlEVrzSc
Jp3CM6YLxHbTa0NXIjlzHWjQEtMw6UDsrDJLDnU8dMbMSQorTTpBY/O/eeXeA05x
5cXAtpNOMwIBBQICAOE=
-----END DH PARAMETERS-----
Download dhparam-small.pem
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PARI/GP

powermod(x, k, m) = lift(Mod(x, m) ^ k);

g = 0x5;
p = 0x94ab27ae97f47a42451512b8e0d12219100858896cdb61459725aad551a89c4853aae9224443d4bfc094f9636b79923625709f7ee83873f996e8e9edeea62e40a3fb5412b92b5980383830c1592b4bc4ca77825596bfe07ccdb4267c99d4dc054fc754e864905724241cd7e8b5537750c3acd3af76ee63fb329b3258339b3fbf6111e53e5115af349c269dc233a60bc476d36b43572239731d68d012d330e940ecac324b0e753c74c6cc490a2b4d3a4163f3bf79e5de034e71e5c5c0b6934e33;
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

$\begin{eqnarray}
p \equiv 0x94ab27ae97f47a42451512b8e0d12219100858896cdb61459725aad551a89c4853aae9224443d4bfc094f9636b79923625709f7ee83873f996e8e9edeea62e40a3fb5412b92b5980383830c1592b4bc4ca77825596bfe07ccdb4267c99d4dc054fc754e864905724241cd7e8b5537750c3acd3af76ee63fb329b3258339b3fbf6111e53e5115af349c269dc233a60bc476d36b43572239731d68d012d330e940ecac324b0e753c74c6cc490a2b4d3a4163f3bf79e5de034e71e5c5c0b6934e33 \\
g \equiv 0x5 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
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