Knowledge Base
Diffie-Hellman Parameter
A-

1536-bit ProFTPD 1.3.2 builtin DH parameter

Summary

Name:
1536-bit ProFTPD 1.3.2 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)
0xd8f50c0a3ef7933d07c57ba52de4f1444ecfe82ed87baebded0f8255e512d4df4abdca17a81adc45acdb68fdec8253928c6ed10b30463441afae0a7e4e29313a57f36ee82683dcf67eb7c55a52e3b72983fd96f19c84f7f64a960001336cf435ab0e5c131a6aedfc53c70479b1f09ab0a2deb489c41a70c94fbb5f84046b7a48fd61a6977353ce64681bde4d0056497052f31515f65557f9601e08e2c5560a946a5452f61d707d8a86ae439d03058023a7bda1d7cd9a0a0594591fb8e01f3c6b
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Generator (g)
0x2
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Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----
MIHHAoHBANj1DAo+95M9B8V7pS3k8UROz+gu2Huuve0PglXlEtTfSr3KF6ga3EWs
22j97IJTkoxu0QswRjRBr64Kfk4pMTpX827oJoPc9n63xVpS47cpg/2W8ZyE9/ZK
lgABM2z0NasOXBMaau38U8cEebHwmrCi3rSJxBpwyU+7X4QEa3pI/WGml3NTzmRo
G95NAFZJcFLzFRX2VVf5YB4I4sVWCpRqVFL2HXB9ioauQ50DBYAjp72h182aCgWU
WR+44B88awIBAg==
-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----
MIHLAoHBANj1DAo+95M9B8V7pS3k8UROz+gu2Huuve0PglXlEtTfSr3KF6ga3EWs
22j97IJTkoxu0QswRjRBr64Kfk4pMTpX827oJoPc9n63xVpS47cpg/2W8ZyE9/ZK
lgABM2z0NasOXBMaau38U8cEebHwmrCi3rSJxBpwyU+7X4QEa3pI/WGml3NTzmRo
G95NAFZJcFLzFRX2VVf5YB4I4sVWCpRqVFL2HXB9ioauQ50DBYAjp72h182aCgWU
WR+44B88awIBAgICAOE=
-----END DH PARAMETERS-----
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PARI/GP

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

g = 0x2;
p = 0xd8f50c0a3ef7933d07c57ba52de4f1444ecfe82ed87baebded0f8255e512d4df4abdca17a81adc45acdb68fdec8253928c6ed10b30463441afae0a7e4e29313a57f36ee82683dcf67eb7c55a52e3b72983fd96f19c84f7f64a960001336cf435ab0e5c131a6aedfc53c70479b1f09ab0a2deb489c41a70c94fbb5f84046b7a48fd61a6977353ce64681bde4d0056497052f31515f65557f9601e08e2c5560a946a5452f61d707d8a86ae439d03058023a7bda1d7cd9a0a0594591fb8e01f3c6b;
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

$\begin{eqnarray}
p \equiv 0xd8f50c0a3ef7933d07c57ba52de4f1444ecfe82ed87baebded0f8255e512d4df4abdca17a81adc45acdb68fdec8253928c6ed10b30463441afae0a7e4e29313a57f36ee82683dcf67eb7c55a52e3b72983fd96f19c84f7f64a960001336cf435ab0e5c131a6aedfc53c70479b1f09ab0a2deb489c41a70c94fbb5f84046b7a48fd61a6977353ce64681bde4d0056497052f31515f65557f9601e08e2c5560a946a5452f61d707d8a86ae439d03058023a7bda1d7cd9a0a0594591fb8e01f3c6b \\
g \equiv 0x2 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
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