A note on the security of threshold implementations with d+1d+1 input shares

Recently, threshold implementations (TI) with $d + 1$ input shares have been proposed at Crypto 2015. This optimization aims for more lightweight TI designs while keeping the glitch-resistance of the original concept. In this note, we consider such an approach and provide preliminary simulation-based evidence, backed by empirical results, of the existence of $d^{\text{th}}$-order leakages. We conclude that, while for first-order TI designs this solution can be overkill due to the extra randomness requirements, higher-order TIs can still benefit from it