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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.
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.
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.
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.
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.
-----BEGIN EC PARAMETERS----- MIIB1gIBATBUBgcqhkjOPQEBAkkSgPc/80dvMTgk4x1HASoAVuhPjRIhMbs75sDx 85dURKSK5Dr24IKs2c0wOU9HNtr2g2elUTFw7gpXj99yGkpIrD7cFU5lZZErMIGW BEkAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABEkAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAABBIGTBAKvWbesNA8rrytz3x6T+GDePyV+DoaGjPYavbrt/7n3VEVQVGqd 9vlkWEdmXYWSNuvbxX2zaLEXhst02l06Hm2MO86HMjFa9kAM79pE9lMfkfhrOi0f s5ikiKVTye/rilLpkSed1BtyDve7e+/7mK7lPoD2eFhMPvIvSH93wodtGy4183rv e5JrV227XePiWHpwAkEjhvipJeKIXiM6nMwWFcDWxjU4ej8LPL4AP61ryXLC5udB lp00xMkgFqhcfNBWIwPEzL5ZlGfCTaEYpf5vzWccAQIJAIVVWEGqrsSs -----END EC PARAMETERS-----
p = 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b; a = 0x0; b = 0x1; E = ellinit([a, b], p); G = [0x2af59b7ac340f2baf2b73df1e93f860de3f257e0e86868cf61abdbaedffb9f7544550546a9df6f9645847665d859236ebdbc57db368b11786cb74da5d3a1e6d8c3bce8732315af640, 0xcefda44f6531f91f86b3a2d1fb398a488a553c9efeb8a52e991279dd41b720ef7bb7beffb98aee53e80f678584c3ef22f487f77c2876d1b2e35f37aef7b926b576dbb5de3e2587a70]; n = 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01; h = 0x85555841aaaec4ac;
$\begin{aligned}
y^2 &\equiv x^3 + a x + b \pmod{p} \\
p &= 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b \\
a &= 0x0 \\
b &= 0x1 \\
G &= (0x2af59b7ac340f2baf2b73df1e93f860de3f257e0e86868cf61abdbaedffb9f7544550546a9df6f9645847665d859236ebdbc57db368b11786cb74da5d3a1e6d8c3bce8732315af640, 0xcefda44f6531f91f86b3a2d1fb398a488a553c9efeb8a52e991279dd41b720ef7bb7beffb98aee53e80f678584c3ef22f487f77c2876d1b2e35f37aef7b926b576dbb5de3e2587a70) \\
n &= 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01 \\
h &= 0x85555841aaaec4ac
\end{aligned}$