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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----- MIICAAIBATBbBgcqhkjOPQEBAlA8uGhlPTALP+gAFVVN0l2w/AHc3pXUAAAAYxu9 QhcVATlVVVVVUpwAXHXWwqsAAAAAAArHlgDSq6qqqqqqqqqT6vP/AAqqqqqqqqqq vqsACzCBpARQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEUAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEBIGhBBYPY6OjspfxEwde15RmE46F sCX3/nJLeOMtevxNc0vdVPhxCSuNGWbUkcD0Wkiou6VYYJXf/MFBC34m7Ra6+YwR F5WRNMJKF6e+MeGvv4RPLTQLM4d0gKl4XobtLtyvwXC4JWjLIbcIt5/G2jdIRh/N gGl+SGaV88rnb8sXgeeE9oEvV74F38hQQmZQ3ti0CkZLAKNXGCKOyOArUrWdh24C NgUPlANf9AAP//////+UBr/cAEAAAAAAAAADX7gB3/v/////////9AG/+AAAAAAA AAAAAA/8AQIbC/+AAVVVVVVVVVVVVNlX6qqqqqqqqqqqqqvr -----END EC PARAMETERS-----
p = 0x3cb868653d300b3fe80015554dd25db0fc01dcde95d4000000631bbd421715013955555555529c005c75d6c2ab00000000000ac79600d2abaaaaaaaaaaaaaa93eaf3ff000aaaaaaaaaaaaaaabeab000b; a = 0x0; b = 0x4; E = ellinit([a, b], p); G = [0x160f63a3a3b297f113075ed79466138e85b025f7fe724b78e32d7afc4d734bdd54f871092b8d1966d491c0f45a48a8bba5586095dffcc1410b7e26ed16baf98c1117959134c24a17a7be31e1afbf844f, 0x2d340b33877480a9785e86ed2edcafc170b82568cb21b708b79fc6da3748461fcd80697e486695f3cae76fcb1781e784f6812f57be05dfc850426650ded8b40a464b00a35718228ec8e02b52b59d876e]; n = 0x50f94035ff4000fffffffffff9406bfdc0040000000000000035fb801dffbfffffffffffffff401bff80000000000000000000ffc01; h = 0xbff8001555555555555555554d957eaaaaaaaaaaaaaaaaaaaabeb;
$\begin{aligned}
y^2 &\equiv x^3 + a x + b \pmod{p} \\
p &= 0x3cb868653d300b3fe80015554dd25db0fc01dcde95d4000000631bbd421715013955555555529c005c75d6c2ab00000000000ac79600d2abaaaaaaaaaaaaaa93eaf3ff000aaaaaaaaaaaaaaabeab000b \\
a &= 0x0 \\
b &= 0x4 \\
G &= (0x160f63a3a3b297f113075ed79466138e85b025f7fe724b78e32d7afc4d734bdd54f871092b8d1966d491c0f45a48a8bba5586095dffcc1410b7e26ed16baf98c1117959134c24a17a7be31e1afbf844f, 0x2d340b33877480a9785e86ed2edcafc170b82568cb21b708b79fc6da3748461fcd80697e486695f3cae76fcb1781e784f6812f57be05dfc850426650ded8b40a464b00a35718228ec8e02b52b59d876e) \\
n &= 0x50f94035ff4000fffffffffff9406bfdc0040000000000000035fb801dffbfffffffffffffff401bff80000000000000000000ffc01 \\
h &= 0xbff8001555555555555555554d957eaaaaaaaaaaaaaaaaaaaabeb
\end{aligned}$