  The underlying fundaments of blockchain are cryptography and cryptographic
concepts that provide reliable and secure decentralized solutions. Although
many recent papers study the use-cases of blockchain in different industrial
areas, such as finance, health care, legal relations, IoT, information
security, and consensus building systems, only few studies scrutinize the
cryptographic concepts used in blockchain. To the best of our knowledge, there
is no Systematization of Knowledge (SoK) that gives a complete picture of the
existing cryptographic concepts which have been deployed or have the potential
to be deployed in blockchain. In this paper, we thoroughly review and
systematize all cryptographic concepts which are already used in blockchain.
Additionally, we give a list of cryptographic concepts which have not yet been
applied but have big potentials to improve the current blockchain solutions. We
also include possible instantiations of these cryptographic concepts in the
blockchain domain. Last but not least, we explicitly postulate 21 challenging
problems that cryptographers interested in blockchain can work on.
