Knowledge Base
Diffie-Hellman Parameter
A+

2048-bit Postfix 3.6 builtin DH parameter

Summary

Name:
2048-bit Postfix 3.6 builtin DH parameter
Key size:
2048 bits

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Security

A+
Key Size
Name

2048

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-----
MIIBEwKCAQwwggEIAoIBAQCeKBXFzJtasOmrdIsqI87qh6AYCdBALJMjXcDpeCxT
2T4hFIlceXMevSMeGGVt0jzrQcq7qZlVhK6ecFclIUKq24LG5vHPt7wqVsxVH63p
aBgi/AliwzIbBR/O7ONttXngiUXz8yajgdlZ7u14vg7d9+/LgT8BtxCPDb4pIRP/
KhMldZns9S1JAR2kE+gsyBNgV5ixBkV3pCT5Jz8I5ptLIDtDaaPMmsQ8Huy3NeRZ
a20q3/cL1FoPeYDhdUwQ6ibw1fOmFak+PQ24U1BJd0lHQznuuIrlFMTjEPv1Uu+l
j6R+V7lf2gAY8HIp1P6QWh8aQO5O+j7zckvqRFNDU1ebAgECAgEC
-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----
MIIBFwKCAQwwggEIAoIBAQCeKBXFzJtasOmrdIsqI87qh6AYCdBALJMjXcDpeCxT
2T4hFIlceXMevSMeGGVt0jzrQcq7qZlVhK6ecFclIUKq24LG5vHPt7wqVsxVH63p
aBgi/AliwzIbBR/O7ONttXngiUXz8yajgdlZ7u14vg7d9+/LgT8BtxCPDb4pIRP/
KhMldZns9S1JAR2kE+gsyBNgV5ixBkV3pCT5Jz8I5ptLIDtDaaPMmsQ8Huy3NeRZ
a20q3/cL1FoPeYDhdUwQ6ibw1fOmFak+PQ24U1BJd0lHQznuuIrlFMTjEPv1Uu+l
j6R+V7lf2gAY8HIp1P6QWh8aQO5O+j7zckvqRFNDU1ebAgECAgECAgIA4Q==
-----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

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