Somewhat tangential, but there are much better options if you're looking for opportunities for optimization. It's literally trying to improve efficiency by skimping on safety features, like trying to save on vehicle weight by removing unnecessary seatbelts or crumple zones. Eliminating side channels concincingly is very difficult, you're just better off taking the tiny performance hit and virtually* eliminating that vector instead of trying to come up with a novel low-density seatbelt.
(I say virtually, because even constant time crypto isn't bulletproof - GoFetch, a recent Apple M-series CPU vulnerability inadvertently broke the "constant" part because of a quirk of the prefetcher. Side channels are hard, no need to make it harder.)
(I say virtually, because even constant time crypto isn't bulletproof - GoFetch, a recent Apple M-series CPU vulnerability inadvertently broke the "constant" part because of a quirk of the prefetcher. Side channels are hard, no need to make it harder.)