An encryption system that uses two related keys where one key encrypts the data and a different, non-interchangeable key decrypts the data is known as symmetric key cryptography.
The premise of the question is a description of asymmetric key cryptography, not symmetric. Asymmetric cryptography, also known as public-key cryptography, uses a pair of keys – a public key for encryption and a private key for decryption. These keys are mathematically related but not identical, and one cannot derive the private key from the public key. Symmetric key cryptography, in contrast, uses the same key for encryption and decryption.
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