Knowledge Base
Diffie-Hellman Parameter
A-

1536-bit ProFTPD 1.3.7 builtin DH parameter

Summary

Name:
1536-bit ProFTPD 1.3.7 builtin DH parameter
Key size:
1536 bits
Publishers:

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Security

A-
Key Size
Name

1536

Security

The Diffie-Hellman ephemeral public key parameter[409][410][411] with prime size less or equal than 2048-bit[423] might be weakened against logjam attack[7][8][9][10], however it will only be able to exploited by a national states.

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+
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)
0xff889f3a0f13f1d479f13a7f7f0e8da006e34b32f7b3fb77a1daf56550a18f86fdda63bae3975c09b40627513ac13b3edf9564a3591775f2e50c3a0ef6e5c3037291fd7f9dd6493bf2044c9f9a7d03222caa7a97f143ab7aa7c4308bf31240fcf8cef5ddc3481661cc124f29ffb653a07657a5359635e06a4851b4e9f02fab91535acaade1d9bfb701d166d0009a49fa9c38f9ab015389495406ba99f5a64461f1caa72f5ca05e9b8665c4f3138ec57762791ecbf15ee81c8023a7ba13fe378b
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Generator (g)
0x2
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Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----
MIHHAoHBAP+InzoPE/HUefE6f38OjaAG40sy97P7d6Ha9WVQoY+G/dpjuuOXXAm0
BidROsE7Pt+VZKNZF3Xy5Qw6DvblwwNykf1/ndZJO/IETJ+afQMiLKp6l/FDq3qn
xDCL8xJA/PjO9d3DSBZhzBJPKf+2U6B2V6U1ljXgakhRtOnwL6uRU1rKreHZv7cB
0WbQAJpJ+pw4+asBU4lJVAa6mfWmRGHxyqcvXKBem4ZlxPMTjsV3Ynkey/Fe6ByA
I6e6E/43iwIBAg==
-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----
MIHLAoHBAP+InzoPE/HUefE6f38OjaAG40sy97P7d6Ha9WVQoY+G/dpjuuOXXAm0
BidROsE7Pt+VZKNZF3Xy5Qw6DvblwwNykf1/ndZJO/IETJ+afQMiLKp6l/FDq3qn
xDCL8xJA/PjO9d3DSBZhzBJPKf+2U6B2V6U1ljXgakhRtOnwL6uRU1rKreHZv7cB
0WbQAJpJ+pw4+asBU4lJVAa6mfWmRGHxyqcvXKBem4ZlxPMTjsV3Ynkey/Fe6ByA
I6e6E/43iwIBAgICAOE=
-----END DH PARAMETERS-----
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PARI/GP

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

g = 0x2;
p = 0xff889f3a0f13f1d479f13a7f7f0e8da006e34b32f7b3fb77a1daf56550a18f86fdda63bae3975c09b40627513ac13b3edf9564a3591775f2e50c3a0ef6e5c3037291fd7f9dd6493bf2044c9f9a7d03222caa7a97f143ab7aa7c4308bf31240fcf8cef5ddc3481661cc124f29ffb653a07657a5359635e06a4851b4e9f02fab91535acaade1d9bfb701d166d0009a49fa9c38f9ab015389495406ba99f5a64461f1caa72f5ca05e9b8665c4f3138ec57762791ecbf15ee81c8023a7ba13fe378b;
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

$\begin{eqnarray}
p \equiv 0xff889f3a0f13f1d479f13a7f7f0e8da006e34b32f7b3fb77a1daf56550a18f86fdda63bae3975c09b40627513ac13b3edf9564a3591775f2e50c3a0ef6e5c3037291fd7f9dd6493bf2044c9f9a7d03222caa7a97f143ab7aa7c4308bf31240fcf8cef5ddc3481661cc124f29ffb653a07657a5359635e06a4851b4e9f02fab91535acaade1d9bfb701d166d0009a49fa9c38f9ab015389495406ba99f5a64461f1caa72f5ca05e9b8665c4f3138ec57762791ecbf15ee81c8023a7ba13fe378b \\
g \equiv 0x2 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
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