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DM-RSA-OAEP: Formal Treatment of a Dual-Modulus Fault-Detection Countermeasure Based on Physical Diversity

Ramamonjy Andriamifidisoa, Rufine Marius Lalasoa · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26642 · cited by 0 works (OpenAlex) · open-access PDF

Portuguese

Revisamos o DM-RSA, uma variante RSA que usa dois módulos independentes, cuja versão original foi quebrada pelo ataque de Håstad e continha uma reivindicação de tolerância de compromisso incorrecta. Damos um tratamento formal de sua variante reparada, DM-RSA-OAEP: (i) uma prova de segurança completa IND-CCA2 no modelo aleatório-oráculo através de um argumento híbrido de dois passos, super-limitando a segurança do esquema por aquela da instância RSA-OAEP subjacente mais fraca, com uma perda de simulação explícita; (ii) um teorema de detecção de falhas em um modelo adversário explícito que cobre computação, falhas de chave e verificação, incluindo ataques de erro seguro, sob uma assunção de diversidade física claramente

Machine translation (Meta M2M100); the English original follows.

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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Topics: Countermeasure, Adversary, Computer security, Scheme (mathematics), Computer science, Diversity (politics)

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