In recent years, significant progress in researching and building quantum computers has been made. A fully-fledged quantum computer would be able to efficiently solve a distinct set of mathematical problems like integer factorization and the discrete logarithm, which are the basis for a wide range of cryptographic schemes. In 2016, NIST announced an open competition with the goal of finding and standardizing suitable algorithms for quantum-resistant cryptography. The standardization effort by NIST is aimed at post-quantum secure KEMs and digital signatures. In this article, two of the to-be-standardized algorithms, Kyber and Dilithium, are presented and some of their mathematical details are outlined. Both algorithms are based on so-called lattices and the thereupon constructed »Learning with Errors«, which we will get to know in the following.
The threat posed by quantum computers to the asymmetric cryptography in use today has been well known in the scientific community for more than 25 years, since Peter Shor published a polynomial algorithm for prime factorization to solve the discrete logarithm on a quantum computer. In recent years, crypto experts have increasingly been warning of the progress that is being made in quantum computing and its relevance for cryptography. Research on post-quantum cryptography (PQC) at the Fraunhofer Institute for Applied and Integrated Security AISEC aims to enable businesses, government bodies and citizens to continue to have access to usable cryptography that will remain secure in the long term so they can keep their data secure. This blog article provides a brief overview of four ongoing projects.