Knowledge Base
Diffie-Hellman Parameter
A-

1536-bit ProFTPD 1.2.8 builtin DH parameter

Summary

Name:
1536-bit ProFTPD 1.2.8 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)
0xda68257f9db53f4205bc79656f196a6f701191f208482be20c15d931e73a50329ffbd656fab4a95f221752722ce35da1a8ef164235c6d964c1b3b34c0990f449efde6499ff3c370a91a49e3827f296131e15a252f1540ced5c38c4ecffe2fa0a41bb485dd354a1ebbd1f68ed2a497f6852b3a0773e19fb44cd4b213e3bbaf6a23637e5fa95b07d7b5896c4c9c0cfd93fa3420bd7be1aa8b55758f4049754b059235f980990c0498540232d213eb007060732fbb991409209ed078005145bc19b
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Generator (g)
0x2
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Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----
MIHHAoHBANpoJX+dtT9CBbx5ZW8Zam9wEZHyCEgr4gwV2THnOlAyn/vWVvq0qV8i
F1JyLONdoajvFkI1xtlkwbOzTAmQ9Env3mSZ/zw3CpGknjgn8pYTHhWiUvFUDO1c
OMTs/+L6CkG7SF3TVKHrvR9o7SpJf2hSs6B3Phn7RM1LIT47uvaiNjfl+pWwfXtY
lsTJwM/ZP6NCC9e+Gqi1V1j0BJdUsFkjX5gJkMBJhUAjLSE+sAcGBzL7uZFAkgnt
B4AFFFvBmwIBAg==
-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----
MIHLAoHBANpoJX+dtT9CBbx5ZW8Zam9wEZHyCEgr4gwV2THnOlAyn/vWVvq0qV8i
F1JyLONdoajvFkI1xtlkwbOzTAmQ9Env3mSZ/zw3CpGknjgn8pYTHhWiUvFUDO1c
OMTs/+L6CkG7SF3TVKHrvR9o7SpJf2hSs6B3Phn7RM1LIT47uvaiNjfl+pWwfXtY
lsTJwM/ZP6NCC9e+Gqi1V1j0BJdUsFkjX5gJkMBJhUAjLSE+sAcGBzL7uZFAkgnt
B4AFFFvBmwIBAgICAOE=
-----END DH PARAMETERS-----
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PARI/GP

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

g = 0x2;
p = 0xda68257f9db53f4205bc79656f196a6f701191f208482be20c15d931e73a50329ffbd656fab4a95f221752722ce35da1a8ef164235c6d964c1b3b34c0990f449efde6499ff3c370a91a49e3827f296131e15a252f1540ced5c38c4ecffe2fa0a41bb485dd354a1ebbd1f68ed2a497f6852b3a0773e19fb44cd4b213e3bbaf6a23637e5fa95b07d7b5896c4c9c0cfd93fa3420bd7be1aa8b55758f4049754b059235f980990c0498540232d213eb007060732fbb991409209ed078005145bc19b;
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

$\begin{eqnarray}
p \equiv 0xda68257f9db53f4205bc79656f196a6f701191f208482be20c15d931e73a50329ffbd656fab4a95f221752722ce35da1a8ef164235c6d964c1b3b34c0990f449efde6499ff3c370a91a49e3827f296131e15a252f1540ced5c38c4ecffe2fa0a41bb485dd354a1ebbd1f68ed2a497f6852b3a0773e19fb44cd4b213e3bbaf6a23637e5fa95b07d7b5896c4c9c0cfd93fa3420bd7be1aa8b55758f4049754b059235f980990c0498540232d213eb007060732fbb991409209ed078005145bc19b \\
g \equiv 0x2 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
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