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# What other algorithm/scheme exisits for asymmetric encryption other than RSA?

RSA seems to be the only scheme I see whenever I look into asymmetric encryption. I am now curious to know if other algorithm/scheme exists for asymmetric encryption other than RSA?

If so , what are these other schemes?

Also any explanation for the popularity of RSA?

ElGamal, ECC encryption, Paillier, and so on? RSA labs effects and it's simplicity. Opinion-based and lack of research even from Wikipedia's list. In the end, we mostly use them key encapsualtion, key exchange, and digital signature, not for encryption. Though, in some cased you may use the algebraic properties to achieve some holomorphic encryption as in RSA and Paillier...
yeah Everywhere I look it looks like RSA and asymmetric encryption are synonymous.
you are wrong, as explained above. RSA is the oldest and most widely used being simplest in some sense, but Elliptic Curve based systems dominate in embedded systems giving the same security for shorter bitlength.
There are many, but (EC)IES is pretty common. Note that a rather large set of asymmetric encapsulation (encryption) algorithms are under eval for the Post Quantum Cryptography project alone. And RSA in itself requires a secure padding scheme, so "RSA" only indicates the RSA-**problem** which it is based on. You've got RSA with PKCS#1 v1.5 padding, OAEP padding, RSA-KEM...
@kodlu but as far as I understand there are no Elliptic Curve based systems that handles encryption. I have seen (EC)IES and this only use the EC part for key sharing, the actual encryption is still done by symmetric encryption.
Your comment applies to all asymmetric systems, including RSA. They are not really intended to be used for message encryption, typically used for encrypting symmetric keys, or other key sharing protocols.
@FinlayWeber: how is ECIES not public key encryption? It has a private key, a public key; it encrypts a message with the public key, and decrypts it with the private key. How it works internally is irrelevant to its public interface and security properties (which is what defines a 'public key encryption system')
@kodlu correct me if i am wrong. RSA can be used to directly encrypt and decrypt. It is not just efficient, hence why it is not used. In (EC)IES, there is no provision for encrypting and decrypting by the EC part. The key sharing part even though is public/private key, is done via Diffie hellman which is not an encrypting/decrypting mechanism.
@poncho it matters if you want to understand a bit more how the internals work. If under the hood, it is symmetric encryption that does the heavy lifting, then that should not be ignored if again one is interested in how things work a bit under the hood
Direct encryption with RSA isn't just inefficient, it's insecure. That's why it's used in hybrid schemes to exchange a symmetric key (RSA-KEM, RSAES:PKCS#1v1.5, or RSAES-OAEP are the RSA-based algorithms for key exchange).
That's not correct. Both RSAES-OAEP and RSA-KEM are secure (RSAES:PKCS#1v1.5 is insecure) . The main reason not to use RSA for encryption is for its inefficiency. If it is for security, then why would it be used in hybrid form to exchange a symmetric key?