Knowledge Base
Elliptic-Curve Parameter
A

secp112r2

Summary

Name:
secp112r2
Long Name:
secp112r2 elliptic curve (112-bit prime field)
Key size:
112 bits
Object identifier:
1.3.132.0.7
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)
0xdb7c2abf62e35e668076bead208b
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Coefficient (a)
0x6127c24c05f38a0aaaf65c0ef02c
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Coefficient (b)
0x51def1815db5ed74fcc34c85d709
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Generator (x)
0x4ba30ab5e892b4e1649dd0928643
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Generator (y)
0xadcd46f5882e3747def36e956e97
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Order (n)
0x36df0aafd8b8d7597ca10520d04b
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Cofactor (h)
0x4
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Representations

PEM

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

p = 0xdb7c2abf62e35e668076bead208b;
a = 0x6127c24c05f38a0aaaf65c0ef02c;
b = 0x51def1815db5ed74fcc34c85d709;
E = ellinit([a, b], p);
G = [0x4ba30ab5e892b4e1649dd0928643, 0xadcd46f5882e3747def36e956e97];
n = 0x36df0aafd8b8d7597ca10520d04b;
h = 0x4;
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LaTeX

$\begin{aligned}
y^2 &\equiv x^3 + a x + b \pmod{p} \\
p &= 0xdb7c2abf62e35e668076bead208b \\
a &= 0x6127c24c05f38a0aaaf65c0ef02c \\
b &= 0x51def1815db5ed74fcc34c85d709 \\
G &= (0x4ba30ab5e892b4e1649dd0928643, 0xadcd46f5882e3747def36e956e97) \\
n &= 0x36df0aafd8b8d7597ca10520d04b \\
h &= 0x4
\end{aligned}$
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