Knowledge Base
Diffie-Hellman Parameter
A-

1536-bit MODP Group/Oakley Group 5 (RFC 3526)

Summary

Name:
1536-bit MODP Group/Oakley Group 5 (RFC 3526)
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)
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485b576625e7ec6f44c42e9a637ed6b0bff5cb6f406b7edee386bfb5a899fa5ae9f24117c4b1fe649286651ece45b3dc2007cb8a163bf0598da48361c55d39a69163fa8fd24cf5f83655d23dca3ad961c62f356208552bb9ed529077096966d670c354e4abc9804f1746c08ca237327ffffffffffffffff
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Generator (g)
0x2
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Representations

PEM

Default private value length
-----BEGIN DH PARAMETERS-----
MIHHAoHBAP//////////yQ/aoiFowjTExmKLgNwc0SkCTgiKZ8x0Agu+pjsTmyJR
Sgh5jjQE3e+VGbPNOkMbMCsKbfJfFDdP4TVtbVHCReSFtXZiXn7G9ExC6aY37WsL
/1y29Aa37e44a/taiZ+lrp8kEXxLH+ZJKGZR7ORbPcIAfLihY78FmNpINhxV05pp
Fj+o/STPX4NlXSPco62WHGLzViCFUrue1SkHcJaWbWcMNU5KvJgE8XRsCMojcyf/
/////////wIBAg==
-----END DH PARAMETERS-----
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Small private value length
-----BEGIN DH PARAMETERS-----
MIHLAoHBAP//////////yQ/aoiFowjTExmKLgNwc0SkCTgiKZ8x0Agu+pjsTmyJR
Sgh5jjQE3e+VGbPNOkMbMCsKbfJfFDdP4TVtbVHCReSFtXZiXn7G9ExC6aY37WsL
/1y29Aa37e44a/taiZ+lrp8kEXxLH+ZJKGZR7ORbPcIAfLihY78FmNpINhxV05pp
Fj+o/STPX4NlXSPco62WHGLzViCFUrue1SkHcJaWbWcMNU5KvJgE8XRsCMojcyf/
/////////wIBAgICAOE=
-----END DH PARAMETERS-----
Download dhparam-small.pem
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PARI/GP

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

g = 0x2;
p = 2^1536 - 2^1472 - 1 + 2^64 * (floor(2^1406 * Pi) + 741804);
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

$\begin{eqnarray}
p \equiv 2^{1536} - 2^{1472} - 1 + 2^{64} * (\lfloor 2^{1406} * \pi \rfloor + 741804) \\
g \equiv 0x2 \\
\\
a \in \mathbb{Z}_q \\
b \in \mathbb{Z}_q \\
\\
A \equiv g^a \pmod{p} \\
B \equiv g^b \pmod{p} \\
\\
S \equiv {(g^{a})}^{b}={(g^{b})}^{a}=g^{ab} \pmod{p}
\end{eqnarray}$
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