Abstract. The National Security Agency (NSA) in August 2015 announced plans to transition to post-quantum algorithms “Currently, Suite B cryptographic algorithms are specified by the National Institute of Standards and Technology (NIST) and are used by NSA’s Information Assurance Directorate in solutions approved for protecting classified and unclassified National Security Systems (NSS). Below, we announce preliminary plans for transitioning to quantum resistant algorithms.” [https://www.nsa.gov/ia/programs/suiteb_cryptography/]

Shortly after the National Institute of Standardization and Technology (NIST) announced a call to select standards for post-quantum public-key cryptosystems.

The academic and industrial communities have suggested as the quantum-resistant primitives: Lattice-based, Multivariate, Code-based, Hash-based, Isogeny-based and group-based primitives.

In this talk I will focus on some ideas of (semi)group-based primitives.The one which was proposed to NIST is by SecureRF company based in Connecticut, among its founders there is a number theorists (Goldfeld) and two group theorists (Anshel and Anshel). They proposed a digital signature using a hard algorithmic problem in braid groups, namely conjugacy problem.

I will then give a survey of some other suggested group-based cryptosystems that could be claimed as post-quantum cryptosystems.

(Joint Seminar on Computational Mathematics and on Semigroups, Automata and Languages)