Knowledge Base
Diffie-Hellman Parameter
A-

1536-bit ProFTPD 1.3.8 builtin DH parameter

Summary

Name:
1536-bit ProFTPD 1.3.8 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)
0x8955c299cc56b02922b85f1a985bea81d426af399dd9405813eb3da47c08e9e380a17dee1a394d57b7c47f02ad018e52fe5b97580e5ca1f8e3999bd48bd1e8dffa5a82da8caa4b1c4a76bd20c95a11990dc068c3b51666d346726d92a69f8ce652973ba663677edf67d730f1104e960a8d8aec53bdfc58b46e365f863de3d295f484c2b3d2f5a336adfde4ae7d475dde2724d045520b2d620db936194fdf6712ced65a6717676322a54f91bc326397bcdeb0712f7cd6b12e6ee3879cec541663
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Generator (g)
0x5
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Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----
MIHHAoHBAIlVwpnMVrApIrhfGphb6oHUJq85ndlAWBPrPaR8COnjgKF97ho5TVe3
xH8CrQGOUv5bl1gOXKH445mb1IvR6N/6WoLajKpLHEp2vSDJWhGZDcBow7UWZtNG
cm2Spp+M5lKXO6ZjZ37fZ9cw8RBOlgqNiuxTvfxYtG42X4Y949KV9ITCs9L1ozat
/eSufUdd3ick0EVSCy1iDbk2GU/fZxLO1lpnF2djIqVPkbwyY5e83rBxL3zWsS5u
44ec7FQWYwIBBQ==
-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----
MIHLAoHBAIlVwpnMVrApIrhfGphb6oHUJq85ndlAWBPrPaR8COnjgKF97ho5TVe3
xH8CrQGOUv5bl1gOXKH445mb1IvR6N/6WoLajKpLHEp2vSDJWhGZDcBow7UWZtNG
cm2Spp+M5lKXO6ZjZ37fZ9cw8RBOlgqNiuxTvfxYtG42X4Y949KV9ITCs9L1ozat
/eSufUdd3ick0EVSCy1iDbk2GU/fZxLO1lpnF2djIqVPkbwyY5e83rBxL3zWsS5u
44ec7FQWYwIBBQICAOE=
-----END DH PARAMETERS-----
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PARI/GP

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

g = 0x5;
p = 0x8955c299cc56b02922b85f1a985bea81d426af399dd9405813eb3da47c08e9e380a17dee1a394d57b7c47f02ad018e52fe5b97580e5ca1f8e3999bd48bd1e8dffa5a82da8caa4b1c4a76bd20c95a11990dc068c3b51666d346726d92a69f8ce652973ba663677edf67d730f1104e960a8d8aec53bdfc58b46e365f863de3d295f484c2b3d2f5a336adfde4ae7d475dde2724d045520b2d620db936194fdf6712ced65a6717676322a54f91bc326397bcdeb0712f7cd6b12e6ee3879cec541663;
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

$\begin{eqnarray}
p \equiv 0x8955c299cc56b02922b85f1a985bea81d426af399dd9405813eb3da47c08e9e380a17dee1a394d57b7c47f02ad018e52fe5b97580e5ca1f8e3999bd48bd1e8dffa5a82da8caa4b1c4a76bd20c95a11990dc068c3b51666d346726d92a69f8ce652973ba663677edf67d730f1104e960a8d8aec53bdfc58b46e365f863de3d295f484c2b3d2f5a336adfde4ae7d475dde2724d045520b2d620db936194fdf6712ced65a6717676322a54f91bc326397bcdeb0712f7cd6b12e6ee3879cec541663 \\
g \equiv 0x5 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
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