DM-RSA-OAEP: Formal Treatment of a Dual-Modulus Fault-Detection Countermeasure Based on Physical Diversity
Abstract
We revisit DM-RSA, an RSA variant that uses two independent moduli, whose original version was broken by Håstad's attack and contained an incorrect compromise-tolerance claim. We give a formal treatment of its repaired variant, DM-RSA-OAEP: (i) a complete IND-CCA2 security proof in the random-oracle model via a two-step hybrid argument, upper-bounding the security of the scheme by that of the weaker underlying RSA-OAEP instance, with an explicit simulation loss; (ii) a fault-detection theorem in an explicit adversary model that covers computation, key, and verification faults, including safe-error attacks, under a clearly stated physical-diversity assumption; (iii) an explicit analysis of why the countermeasure degrades to uselessness when the diversity assumption is violated (common-mode faults on a single chip). We position the scheme against the countermeasure landscape and against the broken dual-modulus literature. The contribution is deliberately framed as a fault countermeasure with a provable detection guarantee, not as a computationally stronger RSA. We conclude with a concrete instantiation and a detailed measurement protocol.
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BibTeX
@misc{andriamifidisoa2026dmrsaoaep,
title = {{DM-RSA-OAEP: Formal Treatment of a Dual-Modulus Fault-Detection Countermeasure Based on Physical Diversity}},
author = {Ramamonjy Andriamifidisoa and Rufine Marius Lalasoa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26642},
eprint = {2610.26642},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26642},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - DM-RSA-OAEP: Formal Treatment of a Dual-Modulus Fault-Detection Countermeasure Based on Physical Diversity
AU - Ramamonjy Andriamifidisoa
AU - Rufine Marius Lalasoa
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26642
UR - https://arxiv.org/abs/2610.26642
AB - We revisit DM-RSA, an RSA variant that uses two independent moduli, whose original version was broken by Håstad's attack and contained an incorrect compromise-tolerance claim. We give a formal treatment of its repaired variant, DM-RSA-OAEP: (i) a complete IND-CCA2 security proof in the random-oracle model via a two-step hybrid argument, upper-bounding the security of the scheme by that of the weaker underlying RSA-OAEP instance, with an explicit simulation loss; (ii) a fault-detection theorem in an explicit adversary model that covers computation, key, and verification faults, including safe-error attacks, under a clearly stated physical-diversity assumption; (iii) an explicit analysis of why the countermeasure degrades to uselessness when the diversity assumption is violated (common-mode faults on a single chip). We position the scheme against the countermeasure landscape and against the broken dual-modulus literature. The contribution is deliberately framed as a fault countermeasure with a provable detection guarantee, not as a computationally stronger RSA. We conclude with a concrete instantiation and a detailed measurement protocol.
ER -