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.
Fabio was born in Rio de Janeiro, Brazil, on February 16, 1975. After finishing the Segundo Grau at Colégio Pinheiro Guimarães, Rio de Janeiro, Brazil, he moved to Germany. In 1997, he started studying applied computer science in Wiesbaden, Germany. He completed his Diploma in 2002. After finishing his diploma studies, he changed to the industry, where he was responsible for the IT and process management departments of two companies for over 15 years. In 2006, he started a master’s degree at the RheinMain University of Applied Sciences, Wiesbaden, Germany. His master studies ended in 2010 with a M.Sc. thesis on distributed computing in the fields of number theory. In 2018, he started his Ph.D. studies on post-quantum cryptography. From 2019, he was an external Ph.D. candidate at the Radboud University, Nijmegen, The Netherlands.