A selection of recent lattice-based signature and encryption schemes

Abstract

It is known that the development of quantum computers will break
the cryptographic schemes that are in use today. Since Shor's algorithm is able
to solve the factoring and discrete logarithm problems, all cryptographic systems
based on these two problems will get broken in the presence of large-scale quantum
computers. Lattice-based schemes, however, are considered secure against attacks
with these new machines. In this paper we present an overview of lattice-based
cryptosystems, showing the most recent and the most promising candidates for
encryption and signatures based on lattice problems. We explain the advantages
and disadvantages of the cryptographic schemes. We also adjoin details about
zero knowledge identication. With this work we try to give insight to one of the
most promising candidates of future cryptography, for the time when potential
quantum computers exist. We also point out drawbacks of these systems, which
discloses directions for future work in lattice-based cryptography.