Hardened CTIDH: Dummy-Free and Deterministic CTIDH

Isogeny-based cryptography has emerged as a promising post-quantum alternative, with CSIDH and its constant-time variant CTIDH offering efficient group-action protocols. dCTIDH recently introduced a efficient deterministic version. However, CTIDH and dCTIDH rely on dummy operations in differential addition chains (DACs) and Matryoshka-isogenies, which can be exploitable by fault-injection attacks. In this work, we present the first dummy-free implementation of dCTIDH. Our approach combines two recent ideas: DACsHUND, which enforces equal-length DACs within each batch without padding, and a reformulated Matryoshka structure that removes dummy multiplications and validates all intermediate points. Our analysis shows that small primes such as 3, 5, and 7 severely restrict feasible DACsHUND configurations, motivating new parameter sets that exclude them. We implement dummy-free dCTIDH-2048-194 and dCTIDH-2048-205, achieving group action costs of roughly 357, 000 to 362, 000 F_p-multiplications, with median evaluation times of 1.59 to 1.60 (Gcyc). These results do not surpass dCTIDH, but they outperform CTIDH by roughly 5% while eliminating dummy operations entirely. Compared to dCSIDH, our construction is more than 4× faster. To the best of our knowledge, this is the first efficient implementation of a CSIDH-like protocol that is simultaneously deterministic, constant-time, and fully dummy-free.