Knowledge Base
Diffie-Hellman Parameter
D

1024-bit Apache 2.0.18 builtin DH parameter

Summary

Name:
1024-bit Apache 2.0.18 builtin DH parameter
Key size:
1024 bits

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Security

D
Key Size
Name

1024

Security

The Diffie-Hellman ephemeral public key parameter[409][410][411] with prime size less or equal than 1024-bit[424] is weakened against logjam attack[7][8][9][10], but can only be exploited by a national states.

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)
0xe6969d3d495be32c7cf180c3bdd4798e91b7818251bb055e2a2064904a79a770fa15a259cbd523a6a6ef09c43048d5a22f971f3c20129b48000e6edd061cbc053e371d794e5327df611ebbbe1bac9b5c6044cf023d76e05eea9bad991b13a63c974e9ef1839eb5db125136f7262e56a8871538dfd823c6505085e21f0dd5c86b
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Generator (g)
0x2
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Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----
MIGHAoGBAOaWnT1JW+MsfPGAw73UeY6Rt4GCUbsFXiogZJBKeadw+hWiWcvVI6am
7wnEMEjVoi+XHzwgEptIAA5u3QYcvAU+Nx15TlMn32Eeu74brJtcYETPAj124F7q
m62ZGxOmPJdOnvGDnrXbElE29yYuVqiHFTjf2CPGUFCF4h8N1chrAgEC
-----END DH PARAMETERS-----
Download dhparam.pem
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Small private value length
-----BEGIN DH PARAMETERS-----
MIGLAoGBAOaWnT1JW+MsfPGAw73UeY6Rt4GCUbsFXiogZJBKeadw+hWiWcvVI6am
7wnEMEjVoi+XHzwgEptIAA5u3QYcvAU+Nx15TlMn32Eeu74brJtcYETPAj124F7q
m62ZGxOmPJdOnvGDnrXbElE29yYuVqiHFTjf2CPGUFCF4h8N1chrAgECAgIA4Q==
-----END DH PARAMETERS-----
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PARI/GP

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

g = 0x2;
p = 0xe6969d3d495be32c7cf180c3bdd4798e91b7818251bb055e2a2064904a79a770fa15a259cbd523a6a6ef09c43048d5a22f971f3c20129b48000e6edd061cbc053e371d794e5327df611ebbbe1bac9b5c6044cf023d76e05eea9bad991b13a63c974e9ef1839eb5db125136f7262e56a8871538dfd823c6505085e21f0dd5c86b;
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

$\begin{eqnarray}
p \equiv 0xe6969d3d495be32c7cf180c3bdd4798e91b7818251bb055e2a2064904a79a770fa15a259cbd523a6a6ef09c43048d5a22f971f3c20129b48000e6edd061cbc053e371d794e5327df611ebbbe1bac9b5c6044cf023d76e05eea9bad991b13a63c974e9ef1839eb5db125136f7262e56a8871538dfd823c6505085e21f0dd5c86b \\
g \equiv 0x2 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
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