Knowledge Base
Elliptic-Curve Parameter
A

secp128r2

Summary

Name:
secp128r2
Long Name:
secp128r2 elliptic curve (128-bit prime field)
Key size:
128 bits
Object identifier:
1.3.132.0.29
Publishers:

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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)
0xfffffffdffffffffffffffffffffffff
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Coefficient (a)
0xd6031998d1b3bbfebf59cc9bbff9aee1
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Coefficient (b)
0x5eeefca380d02919dc2c6558bb6d8a5d
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Generator (x)
0x7b6aa5d85e572983e6fb32a7cdebc140
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Generator (y)
0x27b6916a894d3aee7106fe805fc34b44
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Order (n)
0x3fffffff7fffffffbe0024720613b5a3
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Cofactor (h)
0x4
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Representations

PEM

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

p = 0xfffffffdffffffffffffffffffffffff;
a = 0xd6031998d1b3bbfebf59cc9bbff9aee1;
b = 0x5eeefca380d02919dc2c6558bb6d8a5d;
E = ellinit([a, b], p);
G = [0x7b6aa5d85e572983e6fb32a7cdebc140, 0x27b6916a894d3aee7106fe805fc34b44];
n = 0x3fffffff7fffffffbe0024720613b5a3;
h = 0x4;
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LaTeX

$\begin{aligned}
y^2 &\equiv x^3 + a x + b \pmod{p} \\
p &= 0xfffffffdffffffffffffffffffffffff \\
a &= 0xd6031998d1b3bbfebf59cc9bbff9aee1 \\
b &= 0x5eeefca380d02919dc2c6558bb6d8a5d \\
G &= (0x7b6aa5d85e572983e6fb32a7cdebc140, 0x27b6916a894d3aee7106fe805fc34b44) \\
n &= 0x3fffffff7fffffffbe0024720613b5a3 \\
h &= 0x4
\end{aligned}$
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