Knowledge Base
Elliptic-Curve Parameter
A

ssc-512

Summary

Name:
ssc-512
Long Name:
MIRACL Standard Secure Curve (512-bit)
Key size:
512 bits
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]. 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)
0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c5ef
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Coefficient (a)
0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c5ec
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Coefficient (b)
0xadf85458a2bb4a9aafdc5620273d3cf1d8b9c583ce2d3695a9e13641146433fbcc939dce249b3ef97d2fe363630c75d8f681b202aec4617ad3df1ed5d5fd6a8d
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Generator (x)
0x1
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Generator (y)
0x300df8fdd73e5eca6c547355cb46e332ea09414413973390c5a4a8044da455ca393b063a8998373e9990903fb9f5be1a9ceebff0e5bb9b10d3e46e27e651fb92
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Order (n)
0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b235a2359c4afbc9eb7987f1c9ab37e42599188c4b7dc6269b830d80897f57a5f71
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Cofactor (h)
0x1
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Representations

PEM

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

p = 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c5ef;
a = 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c5ec;
b = 0xadf85458a2bb4a9aafdc5620273d3cf1d8b9c583ce2d3695a9e13641146433fbcc939dce249b3ef97d2fe363630c75d8f681b202aec4617ad3df1ed5d5fd6a8d;
E = ellinit([a, b], p);
G = [0x1, 0x300df8fdd73e5eca6c547355cb46e332ea09414413973390c5a4a8044da455ca393b063a8998373e9990903fb9f5be1a9ceebff0e5bb9b10d3e46e27e651fb92];
n = 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b235a2359c4afbc9eb7987f1c9ab37e42599188c4b7dc6269b830d80897f57a5f71;
h = 0x1;
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LaTeX

$\begin{aligned}
y^2 &\equiv x^3 + a x + b \pmod{p} \\
p &= 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c5ef \\
a &= 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c5ec \\
b &= 0xadf85458a2bb4a9aafdc5620273d3cf1d8b9c583ce2d3695a9e13641146433fbcc939dce249b3ef97d2fe363630c75d8f681b202aec4617ad3df1ed5d5fd6a8d \\
G &= (0x1, 0x300df8fdd73e5eca6c547355cb46e332ea09414413973390c5a4a8044da455ca393b063a8998373e9990903fb9f5be1a9ceebff0e5bb9b10d3e46e27e651fb92) \\
n &= 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b235a2359c4afbc9eb7987f1c9ab37e42599188c4b7dc6269b830d80897f57a5f71 \\
h &= 0x1
\end{aligned}$
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