Here is more information on Shor’s algorithm for fast factorisation by a quantum computer. Although not discussed in the video, other public key systems such as elliptic curve cryptography are also vulnerable to quantum computing.
A variety of algorithms are under consideration for quantum-safe cryptography. A project has been underway since 2016 at the U.S. National Institute of Standards and Technology, the “NIST Post-Quantum Cryptography Standardization”, to develop and eventually standardise one or more quantum-safe algorithms. The Open Quantum Safe project has developed a library which implements a number of candidate algorithms and may be integrated with OpenSSL for applications.
It is important to note that the “quantum threat to encryption” affects primarily the distribution of keys in public key cryptosystems. Symmetric encryption, where a secret key is distributed via a separate secure channel and hashing algorithms, used for authentication and the foundation of cryptocurrency systems, are largely unaffected by the advent of quantum computing.