Rsa Security

The subject of rsa security encompasses a wide range of important elements. public key - How big an RSA key is considered secure today .... Thus, to attain security against all attacks known or plausibly imaginable today including adversaries with large quantum computers, cryptographers recommend one-terabyte RSA moduli of 4096-bit primes. Cryptographers also recommend that you brush your teeth and floss twice a day. Additionally, aES vs RSA - Which is stronger given two scenarios?. Any thoughts about ciphertext-only attacks (COA) are pretty much futile from a modern point of view: If an encryption scheme offers only COA-security, it is utterly broken.

And any stronger security propertly is implicitly COA-resistant as well. Security strength of RSA in relation with the modulus size. As for the reasoning behind the larger key sizes for RSA, the explanation's not too difficult. 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). In relation to this, how does RSA signature verification work?.

Concluding RSA encrypted messages as signatures can be insufficient depending on the scenario, thus hash functions are commonly used in digital signature generation and additionally @poncho's answer is of relevance too. Wikipedia articles on homomorphic encryption and module homomorphism dive into detail of this aspect of RSA encryption: In this context, definition of textbook RSA - Cryptography Stack Exchange. What is the definition of textbook or "raw" RSA?

What are some of the properties of textbook RSA? How does it differ from other schemes based on RSA? In relation to this, how are primes generated for RSA? - Cryptography Stack Exchange.

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). From another angle, how many bits of symmetric security does RSA-3072 actually provide?.

I know that the sizes are standardized to $1024$, $2048$ etc. but they actually provide different security than $128$, $256$... for example $\texttt {RSA-}2048$ is actually $112$ bits of security and $128$ bits would be $2304$, so how many bits of security is $\texttt {RSA-}3072$ actually providing?

When to use RSA and when ElGamal asymmetric encryption. Similarly, 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. Additionally, why does RSA need p and q to be prime numbers?. Despite having read What makes RSA secure by using prime numbers?, I seek clarification because I am still struggling to really grasp the underlying concepts of RSA.

Specifically, why can't we cho...