Dilithium digital signature scheme

Abstract

The development of quantum computers is a threat to current cryptographic algorithms, such as the RSA algorithm. Due to this, the development of post quantum cryptography is a topic of research. One digital signature algorithm that is proposed as a quantum proof solution is the Dilithium digital signature system. Dilithium is based on a learning with errors problem (LWE) in which the value of generated signatures includes an error term. The security of Dilithium is based on previous re- search on topics such as the Module LWE problem, the Fiat Shamir transformation with aborts and the Module Short integer solution problem (MSIS ). The reference implementation includes optimization in the signature generation process. By using the number theoretic transform the multiplication of the ring elements is point-wise or in other words in linear time. This thesis presents the mathematical foundations on which the systems security is based on. In addition, the security of digital signatures, identification schemes and the LWE problem are discussed. In the final chapter these topics are brought together to present the Dilithium scheme.