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Public-key cryptography requires an asymmetric generation process: deriving the public key from the private key must be easy, but recovering the private key from the public key must be computationally hard.

Conditions: There must be an easy direction from private key to public key.; There must be a computationally hard reverse direction from public key to private key.

Public-key cryptography requires an asymmetric generation process: deriving the public key from the private key must be easy, but recovering the private key from the public key must be computationally hard.

Conditions: There must be an easy direction from private key to public key.; There must be a computationally hard reverse direction from public key to private key.