Knowledge Base
Diffie-Hellman Parameter
C

2048-bit MODP Group with 224-bit Prime Order Subgroup (RFC 5114)

Summary

Name:
2048-bit MODP Group with 224-bit Prime Order Subgroup (RFC 5114)
Key size:
2048 bits
Publishers:

Check your host!

Type a URL to analyze a service

Get a prompt and clear overview of your security configuration. Right now!

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].

C
Prime
Name

Unsafe Prime

Security

The Diffie-Hellman ephemeral public key parameter[409][410][411] contains a non-safe prime[176], so a connection may be vulnerable to a small subgroup confinement attack[72][73].

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
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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
Copy to clipboard
Generator (g)
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
Copy to clipboard

Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----
MIICCgKCAQEArRB+HpEjqdDWYPqnlVnFH6INZOVoO5/RtUsVl7YdCnXm+hQd+VpW
26+aPEB7od8V6z1oijCcGA4d5rhaEnSgpm0/gVKtasISkDfJ7e/aTfjZHo/vVbc5
S3rVt9C2wSIHyfmNEe002/bGugssi7wnvmoA4KC5xJcIs7+KMXCRiDaBKGEwvImF
2xYC5xRBXZMwJ4Jzx94x79xzEPcSH9WgdBWYfZrcCkhtzfk6zEQyg4cxXXXhmMZB
pIDNhqG55YfovmDmnMkosrnFIXLkEwQumyPxCw4W55djybU9z0uoCinj+3PBa451
uX7zY+L/ox9xz53lOE5xuBwKxN/+DBDmTwKCAQEArEAy708tmuOd8wtcj/2sUGze
vnuJmYyvdIZqCM/k/+OmgkpOELmm8N2SHwGnDEr6q3OddwDCn1LFfbF8YgqGUr5e
kAGo1mrXwXZpEBmZAkr00CcnWsE0i7inYtBSG8mK4kcVBCLqHtQJk51U2nRgzbX2
xrJQcXy+8YDrNBGOmNEZUppF1vg0Vm4wJeMWozDvu3eobwwasVsFGuPUKMj4rLcK
gTcVC47rEOGD7dGZY93Z4mPkdwWJ72qiHn9fL/OBtTnM40CdE81Wavu0jWwBkYHh
vP6UswJp7f5y/ptqpL17Wg8ccc//TBnEGOH27AF5gbwIfypwZbOEuJDTGR8r+g==
-----END DH PARAMETERS-----
Download dhparam.pem
Copy to clipboard
Small private value length
-----BEGIN DH PARAMETERS-----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-----END DH PARAMETERS-----
Download dhparam-small.pem
Copy to clipboard

PARI/GP

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

g = 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;
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);
Copy to clipboard

LaTeX

$\begin{eqnarray}
p \equiv 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 \\
g \equiv 0xac4032ef4f2d9ae39df30b5c8ffdac506cdebe7b89998caf74866a08cfe4ffe3a6824a4e10b9a6f0dd921f01a70c4afaab739d7700c29f52c57db17c620a8652be5e9001a8d66ad7c17669101999024af4d027275ac1348bb8a762d0521bc98ae247150422ea1ed409939d54da7460cdb5f6c6b250717cbef180eb34118e98d119529a45d6f834566e3025e316a330efbb77a86f0c1ab15b051ae3d428c8f8acb70a8137150b8eeb10e183edd19963ddd9e263e4770589ef6aa21e7f5f2ff381b539cce3409d13cd566afbb48d6c019181e1bcfe94b30269edfe72fe9b6aa4bd7b5a0f1c71cfff4c19c418e1f6ec017981bc087f2a7065b384b890d3191f2bfa \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
Copy to clipboard