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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----- MIIBoAIBATBLBgcqhkjOPQEBAkBFMazR/gAjx1UNJntrL+6AkisUsv+5DwTU63wJ tdLRXfHYUnQa9HBKBFgEfoDkVG01uDNvrCJN2BZku/UovmNzMIGEBEAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAHBEAc/wgGoxEW2inYz6VOV+t0i8Xzd+SUAP3XiLZJ7KGsQ2GDQBOy rXMiSAqJyljgz3S8nlQMKt1ol/rQowhPMCrcBIGBBCTRnMZFcu4w85a/brv9emxS E7Oz1wV8yCX5EJOmjNdi/WBhEmLNg43Gtgqn7ugE4ovISZd/rDO0tTDxsSAkipor sxKkO9LObg0CBhPIV6zdz78GHpHl8sPzJEfCWfObLIOrFW138Ulr9+szUeHuTkPc Ghi5GyRkC227kssa3TceAkBFMazR/gAjx1UNJntrL+6AkisUsv+5DwTU63wJtdLR XagvLX7LHbrHGZBcXuzEI/HYbiXtviPFldZEqvGH5ubfAgEB -----END EC PARAMETERS-----
p = 0x4531acd1fe0023c7550d267b6b2fee80922b14b2ffb90f04d4eb7c09b5d2d15df1d852741af4704a0458047e80e4546d35b8336fac224dd81664bbf528be6373; a = 0x7; b = 0x1cff0806a31116da29d8cfa54e57eb748bc5f377e49400fdd788b649eca1ac4361834013b2ad7322480a89ca58e0cf74bc9e540c2add6897fad0a3084f302adc; E = ellinit([a, b], p); G = [0x24d19cc64572ee30f396bf6ebbfd7a6c5213b3b3d7057cc825f91093a68cd762fd60611262cd838dc6b60aa7eee804e28bc849977fac33b4b530f1b120248a9a, 0x2bb312a43bd2ce6e0d020613c857acddcfbf061e91e5f2c3f32447c259f39b2c83ab156d77f1496bf7eb3351e1ee4e43dc1a18b91b24640b6dbb92cb1add371e]; n = 0x4531acd1fe0023c7550d267b6b2fee80922b14b2ffb90f04d4eb7c09b5d2d15da82f2d7ecb1dbac719905c5eecc423f1d86e25edbe23c595d644aaf187e6e6df; h = 0x1;
$\begin{aligned}
y^2 &\equiv x^3 + a x + b \pmod{p} \\
p &= 0x4531acd1fe0023c7550d267b6b2fee80922b14b2ffb90f04d4eb7c09b5d2d15df1d852741af4704a0458047e80e4546d35b8336fac224dd81664bbf528be6373 \\
a &= 0x7 \\
b &= 0x1cff0806a31116da29d8cfa54e57eb748bc5f377e49400fdd788b649eca1ac4361834013b2ad7322480a89ca58e0cf74bc9e540c2add6897fad0a3084f302adc \\
G &= (0x24d19cc64572ee30f396bf6ebbfd7a6c5213b3b3d7057cc825f91093a68cd762fd60611262cd838dc6b60aa7eee804e28bc849977fac33b4b530f1b120248a9a, 0x2bb312a43bd2ce6e0d020613c857acddcfbf061e91e5f2c3f32447c259f39b2c83ab156d77f1496bf7eb3351e1ee4e43dc1a18b91b24640b6dbb92cb1add371e) \\
n &= 0x4531acd1fe0023c7550d267b6b2fee80922b14b2ffb90f04d4eb7c09b5d2d15da82f2d7ecb1dbac719905c5eecc423f1d86e25edbe23c595d644aaf187e6e6df \\
h &= 0x1
\end{aligned}$