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The iterative conditional branchings appear in various sensitive algorithms,like the modular exponentiation in the RSA cryptosystem or the scalarmultiplication in ellipticcurve cryptography. In this paper, we abstract awaythe desirable security properties achieved by the Montgomery ladder, andformalize systems of equations necessary to obtain what we call thesemi-interleaved and fully-interleaved ladder properties. This fruitfulapproach allows us to design novel fault-injection attacks, able to obtainsome/all bits of the secret against different ladders, including the commonMontgomery ladder. We also demonstrate the generality of our approach byapplying the ladder equations to the modular exponentiation and the scalarmultiplication, both in the semi-and fully-interleaved cases, thus proposingnovel and more secure algorithms.

A Hole in the Ladder: Interleaved Variables in Iterative Conditional Branching (Extended Version)