Hardened CTIDH: Dummy-Free and Deterministic CTIDH
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| Format: | Preprint |
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2025
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| _version_ | 1866914039879172096 |
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| author | Banegas, Gustavo Hellenbrand, Andreas Saldanha, Matheus |
| author_facet | Banegas, Gustavo Hellenbrand, Andreas Saldanha, Matheus |
| contents | Isogeny-based cryptography has emerged as a promising postquantum 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 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 dC-TIDH, but they outperform CTIDH by roughly 5% while eliminating dummy operations entirely. Compared to dCSIDH, our construction is more than 4x 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_12877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hardened CTIDH: Dummy-Free and Deterministic CTIDH Banegas, Gustavo Hellenbrand, Andreas Saldanha, Matheus Cryptography and Security Isogeny-based cryptography has emerged as a promising postquantum 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 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 dC-TIDH, but they outperform CTIDH by roughly 5% while eliminating dummy operations entirely. Compared to dCSIDH, our construction is more than 4x 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. |
| title | Hardened CTIDH: Dummy-Free and Deterministic CTIDH |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2509.12877 |