Knowledge Base
Elliptic-Curve Parameter
A

numsp384d1

Summary

Name:
numsp384d1
Long Name:
numsp384d1
Key size:
384 bits
Aliases:
w-384-mers

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Security

A+
Key Size
Security

The elliptic-curve cryptography[118][119][120][121] is an approach to public-key cryptography[164][165][166] based on the elliptic curve[116][117]s. The most important property in terms of encryption strength, beyond the designer is elliptic curve key size[292][293][294]. All the key sizes available are considered secure, so there is no consideration about it.

A+
Trusted Design
Security

The elliptic-curve cryptography[118][119][120][121] is an approach to public-key cryptography[164][165][166] based on the elliptic curve[116][117]s. Note that there is controversy[287][288][289][290][291] around some of the National Institute of Standards and Technology[470][471] designed elliptic curveselliptic curves designed by NIST[285][286]. This elliptic curve designed by independent researcher[284] Daniel J. Bernstein[476][477] and there is no evidence for any compromise.

Recommendations

Add at least one elliptic curve to the list of elliptic curves supported by your server designed by independent researchers and prefer them as server configuration makes it possible.

A
Post-Quantum
Security

The elliptic curve[116][117] cryptography provides no protection against a cryptanalytic attack by a quantum computer, and no classical elliptic curve does — just as classical Diffie-Hellman does not — 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)
0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec3
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Coefficient (a)
0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec0
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Coefficient (b)
0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff77bb
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Generator (x)
0x2
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Generator (y)
0x3c9f82cb4b87b4dc71e763e0663e5dbd8034ed422f04f82673330dc58d15ffa2b4a3d0bad5d30f865bcbbf503ea66f43
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Order (n)
0xffffffffffffffffffffffffffffffffffffffffffffffffd61eaf1eeb5d6881beda9d3d4c37e27a604d81f67b0e61b9
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Cofactor (h)
0x1
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Representations

PEM

-----BEGIN EC PARAMETERS-----
MIIBQAIBATA8BgcqhkjOPQEBAjEA////////////////////////////////////
//////////////////////////7DMGQEMP//////////////////////////////
///////////////////////////////+wAQw////////////////////////////
/////////////////////////////////3e7BGEEAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACPJ+Cy0uHtNxx52PgZj5dvYA0
7UIvBPgmczMNxY0V/6K0o9C61dMPhlvLv1A+pm9DAjEA////////////////////
////////////1h6vHutdaIG+2p09TDfiemBNgfZ7DmG5AgEB
-----END EC PARAMETERS-----
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PARI/GP

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec3;
a = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec0;
b = 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff77bb;
E = ellinit([a, b], p);
G = [0x2, 0x3c9f82cb4b87b4dc71e763e0663e5dbd8034ed422f04f82673330dc58d15ffa2b4a3d0bad5d30f865bcbbf503ea66f43];
n = 0xffffffffffffffffffffffffffffffffffffffffffffffffd61eaf1eeb5d6881beda9d3d4c37e27a604d81f67b0e61b9;
h = 0x1;
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LaTeX

$\begin{aligned}
y^2 &\equiv x^3 + a x + b \pmod{p} \\
p &= 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec3 \\
a &= 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec0 \\
b &= 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff77bb \\
G &= (0x2, 0x3c9f82cb4b87b4dc71e763e0663e5dbd8034ed422f04f82673330dc58d15ffa2b4a3d0bad5d30f865bcbbf503ea66f43) \\
n &= 0xffffffffffffffffffffffffffffffffffffffffffffffffd61eaf1eeb5d6881beda9d3d4c37e27a604d81f67b0e61b9 \\
h &= 0x1
\end{aligned}$
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