First of all, thanks for writing this book. I’ve been only reading the chapter “Asymmetric Key Cipher”, but already learned a lot. And I think it’s easy to follow!
Btw (minor thing), a typo in the sentence "if we encrypt data by a private key, we will be able to decrypt the ciphertext later by the corresponding public key”. I believe you meant the other way around.
The main thing I’m questioning is the statement "The elliptic curve cryptography (ECC) does not directly provide encryption method”.
As far as I understand, ECC is similar to the discrete log problem. The idea is also that with x, g^x is easy to commute but the reverse is hard. Therefore, we should be able to apply the very same idea as in ElGamal encryption (https://en.wikipedia.org/wiki/ElGamal_encryption) to achieve the public key encryption “directly”.
Practically, it’s probably a minor point anyway, my guess is people use ECIES more. But technically, ECC should achieve public key encryption in a straightforward way.
Thanks for your time for reading!
Hi Svetlin,
First of all, thanks for writing this book. I’ve been only reading the chapter “Asymmetric Key Cipher”, but already learned a lot. And I think it’s easy to follow!
Have a question about this particular section https://cryptobook.nakov.com/asymmetric-key-ciphers/ecc-encryption-decryption
Btw (minor thing), a typo in the sentence "if we encrypt data by a private key, we will be able to decrypt the ciphertext later by the corresponding public key”. I believe you meant the other way around.
The main thing I’m questioning is the statement "The elliptic curve cryptography (ECC) does not directly provide encryption method”. As far as I understand, ECC is similar to the discrete log problem. The idea is also that with x, g^x is easy to commute but the reverse is hard. Therefore, we should be able to apply the very same idea as in ElGamal encryption (https://en.wikipedia.org/wiki/ElGamal_encryption) to achieve the public key encryption “directly”.
Practically, it’s probably a minor point anyway, my guess is people use ECIES more. But technically, ECC should achieve public key encryption in a straightforward way. Thanks for your time for reading!
Best, Yi-Hsiu