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Cryptographers also recommend that you brush your teeth and floss twice a day. I know that the sizes are standardized to $1024$, $2048$ etc As for the reasoning behind the larger key sizes for rsa, the explanation's not too difficult

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If you look at the document in the question, you will notice that the bits of security for block ciphers correlate almost perfectly with the size (in bits) of the keys for that block cipher (with rare exceptions). Signature verification, as opposed to signature generation) are faster with rsa. In the block you normally encrypt a random symmetric data key, which is used to encrypt the actual plain text.

The security aspect is based on the fact that it's difficult to factor it back into p and q

Now, since rsa keys are so large (often 1024 bits and above), the primes have to be at least half that (at least 512 bits then). By the way, it's not clear if your question is about the correctness of rsa or the security of rsa (i.e Does rsa need to have a modulus with two prime factors to be correct vs does rsa need to have a modulus with two prime factors to be secure). Rsa encryption whose security is based on the infeasibility of solving the factoring of big primes problem and the elgamal encryption which is as secure as the discrete logarithmic problem

The question is whether or not there are specific circumstances where you must use elgamal instead rsa and vice versa. Why is prime number size important for rsa security Ask question asked 6 years, 4 months ago modified 6 years, 4 months ago The only scientifically established advantaged of rsa over elliptic curves cryptography is that public key operations (e.g