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Yes a brute force key-guessing attack would be faster, but: It would be ridiculously slow for either. E.g. see this for 256-bit keys. There are faster attacks on both and those attacks break larger RSA sizes than ECC sizes. Related: Why can ECC key sizes be smaller than RSA keys for similar security?


Yes, RSA is an example of a cryptosystem where this is possible. The message is encrypted using the recipient's public key only and even the sender could not decrypt it. However, in the comments you mention that you would like to minimize storage requirements. RSA would require e.g. 2048 bits for just the message. In comparison, with ECIES sending a ...


Generate a random symmetric key (for example an AES key). We will use it only once for this transmission, and call it the session key. encrypt the session key with the public key encrypt the message with the session key forget the session key transmit the two encrypted message to the recipient Since you are using a whole new encryption key for every ...


Strictly speaking EdDSA, as defined in "EdDSA for more curves" by Bernstein, Lange et al., can only work for (twisted) Edwards Curves. Thus, IMHO, the correct answer your question is no. In the paper, they define the curve parameters as being the parameters of a (twisted) Edwards curve, the addition law as the addition law on twisted Edwards curves, etc. ...

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