Public Key Cryptography
Full Title or Meme
Public key cryptography relies on certain mathematical problems that are very hard to solve, such as factoring large numbers that are the product of large prime numbers or finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base point. If you know the private key components, you can sign the document or decrypt the data. If you don't have the private key and cannot solve the math, you cannot sign the document or decrypt the data.
Symmetric algorithms offer efficient processing for confidentiality and integrity, but key management (i.e., establishing and maintaining secrets known only to the communicating parties) poses a challenge. Symmetric algorithms offer weak proofs of origin since either party to an exchange can calculate the transformation. Asymmetric algorithms generally require more processing operations and time than are practical for providing confidentiality protection for more than very small volumes of data. However, these algorithms are practical for cryptographic key establishment and Digital Signature processes. In the case of public-key cryptography, one of the keys in a pair can be made public, and distribution of private keys is not needed. Asymmetric key algorithms can be used to establish pairwise keys and authenticate an entity and/or data source in many-to-many communications without demanding a secret channel for key distribution. As a result, most cryptographic entity or data source authentication and key establishment functions use public-key cryptography. 
- Find an asymmetric mathematical algorithm that is easy if you have the private key, but statistically impossible if you do not.
- Existing cryptographic algorithms, like RSA or Elliptic Curve, work well today with compute power available to all.
- Successful Quantum Computing creates an existential threat to existing algorithms since quantum computing algorithms exist to crack traditionally intractable solutions like RSA.
- Find new asymmetric mathematical algorithm that is not susceptible to cracking with quantum computing.
- Revert to secret key algorithms which appear to be immune to cracking with quantum computing.
- William Barker + 2, Getting Ready for Post-Quantum Cryptography: NIST 2021-04-28 https://nvlpubs.nist.gov/nistpubs/CSWP/NIST.CSWP.04282021.pdf