Knowledge Base
Elliptic-Curve Parameter
A

secp224r1

Summary

Name:
secp224r1
Long Name:
secp224r1 elliptic curve (224-bit prime field)
Key size:
224 bits
Object identifier:
1.3.132.0.33
Aliases:
P-224, WAP-WSG-IDM-ECID-WTLS12, ANSIP224R1, ECPRGF224Random, 224-bit Random ECP Group

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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].

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)
0xffffffffffffffffffffffffffffffff000000000000000000000001
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Coefficient (a)
0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe
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Coefficient (b)
0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4
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Generator (x)
0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21
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Generator (y)
0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34
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Order (n)
0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d
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Cofactor (h)
0x1
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Representations

PEM

-----BEGIN EC PARAMETERS-----
BgUrgQQAIQ==
-----END EC PARAMETERS-----
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PARI/GP

p = 0xffffffffffffffffffffffffffffffff000000000000000000000001;
a = 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe;
b = 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4;
E = ellinit([a, b], p);
G = [0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21, 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34];
n = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d;
h = 0x1;
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LaTeX

$\begin{aligned}
y^2 &\equiv x^3 + a x + b \pmod{p} \\
p &= 0xffffffffffffffffffffffffffffffff000000000000000000000001 \\
a &= 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe \\
b &= 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4 \\
G &= (0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21, 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34) \\
n &= 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d \\
h &= 0x1
\end{aligned}$
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