*Basic

Asymmetric cryptography or public-key cryptography is a cryptographic system that uses pairs of keys.[1] Each pair consists of a public key, which may be known to others, and a private key, which will be known only to the owner.[2] Effective security requires keeping the private key private; the public key can be openly distributed without compromising security.[3]

**Intermediate

In such a system, any person can encrypt a message using the intended receiver's public key, but that encrypted message can only be decrypted iwth the receiver's private key.[4] Before the mid-1970s all cipher systems used symmetric key algorithms, in which the same cryptographic key was used with the under underlying algorithm by both the sender and the recipient.[5] By contrast, in the public key system, the public keys can be disseminated widely and openy, and only the corresponding private keys need to be kept secret.[6] Two of the best-known uses of public key encryption are:[7]
Public key encryption: in which a message is encrypted with the intended recipient's public key.
Digital signatures: in which a message is signed with the sender's private key and can be verified by anyone who has access to the sender's public key.

***Advanced

Non-repudiation systems use digital signatures to ensure that one party cannot successfully dispute its authorship of a document or communication. Aside from the poor choice of an asymmetric key algorithm or too short a key length, the chief security risk is that the private key of a pair become known. All security of messages, authentication etc will then be lost.[8]

Sources

[1] Editors. Asymmetric Encryption. OKTA. Okta.com
[2] Editors. Symmetric vs Asymmetric Encryption: What's the difference? Trent on Systems. Trentonsystems.com
[3] Editors. What is Asymmetric Encryption? Cheapssisecurity.com
[4] Editors. Asymmetric Cryptography. Science Direct. Sciencedirect.com
[5] Editors. When to use symmetric encryption vs asymmetric encryption. Key Factor. Keyfactor.com
[6] Editors. What is Asymmetric Cryptography? Tech Target. Techtarget.com
[7] [8] Editors. Asymmetric Encryption. Wikipedia. en.wikipedia.org