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The ECDLP is intractable; for a given field size, it is vastly harder to find k from kP and P than it is to find kP from k and P. k is thus used as the private key; kP is used as the public. The ECDLP is widely believed to be resistant to Number Field Sieve attacks. The best known attack is Pollard’s Rho—whose difficulty grows more rapidly with the field size than do NFS methods. |