Knowledge Base
Diffie-Hellman Parameter
A+

4096-bit HAProxy 1.6 builtin DH parameter

Summary

Name:
4096-bit HAProxy 1.6 builtin DH parameter
Key size:
4096 bits
Publishers:

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Security

A+
Key Size
Name

4096

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)
0x2
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Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----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-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----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-----END DH PARAMETERS-----
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PARI/GP

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

g = 0x2;
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

$\begin{eqnarray}
p \equiv 0xde1694cd995807f1f73296110482d48472809906caf0a36807ce6450e7744520805e4dada5b6edfa806c3b35c49a146b32bbfd1f178eb71fd6fa3f7bee16a562330dedbc4e58e5474de9ab8e38d36e9057e3221533bdf64345b5100abe2cb435b8538dadfba71f8558417a792068b3e13d0876bf860d49e382718cb48d8184d4e7be91dc2639480f35c4ca65e340935276587ddd5175dc6961bf472c16682dc929d3e6c09948a09ac878c06d816712613f71ba411f6c894403ba3b3960aa285559aeb8facb6fa51af72bdd528a8be271a65e7ed82e18e066dfdd2221995273a63320650e53e76b9bc5a32f976576d347237712b6117b24edf1efc0e2a37e67053e964d45c218d1739e07f3816e5263f62076b913d26530181609169e8ff1d2105ad3d4af1661da552e185e1408542e2a25a21a9b8b32a9fdc24896e180cae92217bbce3e9eedc7f11fec1721dc7b82488ebb4b9d5b0404dadb39df0140c3aa26238975c60bd0a2606af1cc6518981b52d27461ccbd60aea3a0666a1634923f41403129c02c63b2078deb94b8e8479252936a1b7e1a61b31bf0d6729bf1b0afbf3e65ef231d6fff70cd8a4c8aa0729dbed4bb24474a68b5f5c6d57acdca064107adc21ee654a7ad03d912c19c13b1c90a438e1e08ce5082735fa7551dd959acb5ea027f6c5b7496986724a30f15fca97d3e67d170f897f367c58c88440802c72b \\
g \equiv 0x2 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
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