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As for other popular public key cryptosystems, no mathematical proof of security has been published for ECC.
However, the U. S. National Security Agency has endorsed ECC by including schemes based on it in its Suite B set of recommended algorithms and allows their use for protecting information classified up to top secret with 384-bit keys.
While the RSA patent expired in 2000, there are patents in force covering certain aspects of ECC technology, though some argue that the Federal elliptic curve digital signature standard ( ECDSA ; NIST FIPS 186-3 ) and certain practical ECC-based key exchange schemes ( including ECDH ) can be implemented without infringing them.

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