Hardened CTIDH: Dummy-Free and Deterministic CTIDH

Isogeny-based cryptography has emerged as a promising post-quantum alternative, with CSIDH and its constant-time variants \ctidh and \dctidh offering efficient group-action protocols. However, \ctidh and~\dctidh rely on dummy operations in differential addition chains (DACs) and Matryoshka, which can be exploitable by fault-injection attacks. In this work, we present the first \emph{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 $357{,}000$–$362{,}000$ $\Fp$-multiplications, with median evaluation times of $1.59$–$1.60$ (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 $4\times$ faster. To the best of our knowledge, this is the first \textit{efficient} implementation of a CSIDH-like protocol that is simultaneously deterministic, constant-time, and fully dummy-free.