Abstract
The security of public-key protocols widely deployed today relies on the hardness of the integer factorization problem and the discrete logarithm problem. Due to Shor’s algorithm these problems can be efficiently solved by a sufficiently large-scale quantum computer. Thus, quantum computers pose a serious threat to today’s digital security. Among other approaches for building quantum-safe algorithms, isogeny-based cryptography is a relatively new approach based on the hardness of finding homomorphisms between elliptic curves. The focus of this thesis lies on optimizations, secure implementations, and applications of isogeny-based cryptography. On the constructive side, we first present and evaluate a hybrid SIDH scheme based on Montgomery and twisted Edwards curves. Further, we introduce two approaches for evaluating CSIDH in constant-time. In particular, we present the first complete constant-time implementation of CSIDH and CTIDH, a new key space and a corresponding new algorithm achieving speed records. On the destructive side, we focus on physical attacks on isogeny-based schemes to understand the security of these schemes against powerful adversaries. Thereby, we present several attacks and possible countermeasures on different isogeny-based schemes and their variants. Finally, we present an actively secure threshold scheme in the setting of hard homogenous spaces.
