Knowledge Base
Diffie-Hellman Parameter
D

1024-bit NGINX 0.7.2 builtin DH parameter

Summary

Name:
1024-bit NGINX 0.7.2 builtin DH parameter
Key size:
1024 bits
Publishers:

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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)
0xbbbc2dcad84674907c43fcf580e9cfdbd958a3f568b42d4b08eed4eb0fb3504c6c030276e710800c5ccbbaa8922614c5beeca565a5fdf1d287a2bc049be6778060e91a92a757e3048f68b076f7d36cc8f29ba5df81dc2ca725ece66270cc9a5035d8ceceef9ea0274a63ab1e58fafd4988d0f65d146757da071df045cfe16b9b
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Generator (g)
0x2
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Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----
MIGHAoGBALu8LcrYRnSQfEP89YDpz9vZWKP1aLQtSwju1OsPs1BMbAMCducQgAxc
y7qokiYUxb7spWWl/fHSh6K8BJvmd4Bg6RqSp1fjBI9osHb302zI8pul34HcLKcl
7OZicMyaUDXYzs7vnqAnSmOrHlj6/UmI0PZdFGdX2gcd8EXP4WubAgEC
-----END DH PARAMETERS-----
Download dhparam.pem
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Small private value length
-----BEGIN DH PARAMETERS-----
MIGLAoGBALu8LcrYRnSQfEP89YDpz9vZWKP1aLQtSwju1OsPs1BMbAMCducQgAxc
y7qokiYUxb7spWWl/fHSh6K8BJvmd4Bg6RqSp1fjBI9osHb302zI8pul34HcLKcl
7OZicMyaUDXYzs7vnqAnSmOrHlj6/UmI0PZdFGdX2gcd8EXP4WubAgECAgIA4Q==
-----END DH PARAMETERS-----
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PARI/GP

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

g = 0x2;
p = 0xbbbc2dcad84674907c43fcf580e9cfdbd958a3f568b42d4b08eed4eb0fb3504c6c030276e710800c5ccbbaa8922614c5beeca565a5fdf1d287a2bc049be6778060e91a92a757e3048f68b076f7d36cc8f29ba5df81dc2ca725ece66270cc9a5035d8ceceef9ea0274a63ab1e58fafd4988d0f65d146757da071df045cfe16b9b;
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

$\begin{eqnarray}
p \equiv 0xbbbc2dcad84674907c43fcf580e9cfdbd958a3f568b42d4b08eed4eb0fb3504c6c030276e710800c5ccbbaa8922614c5beeca565a5fdf1d287a2bc049be6778060e91a92a757e3048f68b076f7d36cc8f29ba5df81dc2ca725ece66270cc9a5035d8ceceef9ea0274a63ab1e58fafd4988d0f65d146757da071df045cfe16b9b \\
g \equiv 0x2 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
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