If you have a trapdoor function, you can use it to make a public-key encryption algorithm: going forward (in the easy direction), the function encrypts going backward (in the hard direction), the function decrypts. A trapdoor function is like a one-way function, but there is a “magic” value that makes the inverse easy to compute. A one-way function is a function that is easy to compute, but whose inverse is hard to compute. This being said, public-key cryptosystems are based on the concept of trapdoor functions. In general, the public key isn't the right type of mathematical object to use for the decryption algorithm, and the private key isn't the right type of mathematical object to use for the encryption algorithm. This symmetry between public keys and private keys does not extend to most other public-key cryptosystems. However, the results are not meaningful according to standard algorithms. (They don't have the same security properties, however - the public key is usually easily guessable from the private key.) You can take an RSA encryption algorithm and feed it a private key, or an RSA decryption algorithm and feed it a public key. With RSA, which is a popular public-key cryptosystem but not the only one, the private key and the public key have the same mathematical properties, so it is possible to use them interchangeably in the algorithms. Similarly, you cannot use a private key to encrypt a message or a public key to decrypt a message. Q: If you pedal backwards on a fish, does it go backwards?Ī fish is not a bicycle.
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