SPP 1079 - Security analysis of cryptographic systems with respect to lattice attacks (Subproject)

Over the last twenty years, cryptography has evolved into a modern key technology with applications ranging from ec cards to electronic signatures on contracts on the Internet. However, the security of many cryptosystems is poorly understood. The project therefore deals with attacks on known public key cryptosystems. The goals of the project can be divided into three levels: 1. Identify possible vulnerabilities of practically relevant cryptosystems: For this purpose, a method mainly based on D. Coppersmith will be used. This procedure is based on the so-called lattice theory from the geometry of numbers. The method has already been successfully used, for example, to identify insecure keys in RSA. Alternatively, we will investigate other lattice-based methods for their applicability in cryptanalysis. 2. further development of lattice-based methods: Here we will develop an automation of Coppersmith's lattice method. Many applications of the method are heuristic. In addition, a classification and extension of provable attacks using the lattice method will be given. 3. new applications of lattice-based attacks: We investigate which algebraic and structural properties cryptosystems must possess in order to be attackable by lattice methods in special cases.

DFG-Procedure Priority Programs

Subproject on SPP 1079: Sicherheit in der Informations- und Kommunikationstechnik