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Asymmetric-key Cryptography

Utilizes a key pair – a public key for encryption and a private key for decryption – enabling secure communication and digital signatures.
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The statement of the theorem

Let MM be the message, PKPK be the public key, and SKSK be the private key. Define the encryption function EPK:{0,1}n→{0,1}mE_{PK}: \{0, 1\}^n \to \{0, 1\}^m and the decryption function DSK:{0,1}m→{0,1}nD_{SK}: \{0, 1\}^m \to \{0, 1\}^n. The system must satisfy:\nDecryption Property: DSK(EPK(M))=M\text{Decryption Property: } D_{SK}(E_{PK}(M)) = M\nKey Separation: The computational difficulty of deriving SK from PK must be intractable.\text{Key Separation: } \text{The computational difficulty of deriving } SK \text{ from } PK \text{ must be intractable.}
Source: Wikipedia