- Scalar multiplication is variable-time, with the variation being correlated with the position of the most significant bit of the exponent (see https://github.com/Bren2010/ecc/blob/bd75261b6fe7839ddc751d6...). An attack like [1] on ECDSA seems plausible.
- The Montgomery ladder uses different code paths depending on whether the exponent bit is 0 or 1; this makes FLUSH+RELOAD attacks possible, as in [2].