![]() The API for encryption says the function takes two arguments: a message and a public key, that is a group element $g^s$ for some secret number $s$ and some group generator $g$. Now, let's be practical: you've got this nice library implementing ElGamal. To encrypt $m$, you draw a random $r$ and compute the ciphertext $(g^r,m*g^)$. ![]() ![]() ![]() How would you do it?īy way of example, take the ElGamal encryption scheme: $s$ is your private key, $g^s$ your public key. To put it simply: there is no meaning for (understand definition for) the wording "encrypt with the private key". As a further hint of how they are intrinsically different, note that it lasted quite a bit of time before ID-based encryption could be designed, whereas ID-based signatures were there from the beginning.) (Encryption for instance, needs to be an injection, whereas signature verification needs to be a surjection towards the verified message space. The security and construction requirements are completely different. Asymmetric encryption and signing are entirely distinct concepts.
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