Knowledge Base
Elliptic-Curve Parameter
A

prime192v1

Summary

Name:
prime192v1
Long Name:
prime192v1 elliptic curve (192-bit prime field)
Key size:
192 bits
Object identifier:
1.2.840.10045.3.1.1
Aliases:
SECP192R1, P-192, ECPRGF192Random, ANSIP192R1, 192-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)
0xfffffffffffffffffffffffffffffffeffffffffffffffff
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Coefficient (a)
0xfffffffffffffffffffffffffffffffefffffffffffffffc
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Coefficient (b)
0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1
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Generator (x)
0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012
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Generator (y)
0x7192b95ffc8da78631011ed6b24cdd573f977a11e794811
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Order (n)
0xffffffffffffffffffffffff99def836146bc9b1b4d22831
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Cofactor (h)
0x1
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Representations

PEM

-----BEGIN EC PARAMETERS-----
BggqhkjOPQMBAQ==
-----END EC PARAMETERS-----
Download ecparam.pem
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PARI/GP

p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff;
a = 0xfffffffffffffffffffffffffffffffefffffffffffffffc;
b = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1;
E = ellinit([a, b], p);
G = [0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, 0x7192b95ffc8da78631011ed6b24cdd573f977a11e794811];
n = 0xffffffffffffffffffffffff99def836146bc9b1b4d22831;
h = 0x1;
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LaTeX

$\begin{aligned}
y^2 &\equiv x^3 + a x + b \pmod{p} \\
p &= 0xfffffffffffffffffffffffffffffffeffffffffffffffff \\
a &= 0xfffffffffffffffffffffffffffffffefffffffffffffffc \\
b &= 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1 \\
G &= (0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, 0x7192b95ffc8da78631011ed6b24cdd573f977a11e794811) \\
n &= 0xffffffffffffffffffffffff99def836146bc9b1b4d22831 \\
h &= 0x1
\end{aligned}$
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