We give one-and two-dimensional scalar multiplication algorithms for Jacobians of genus 2 curves that operate by projecting to Kummer surfaces, where we can exploit faster and more uniform pseudo-multiplication, before recovering the proper "signed" output back on the Jacobian. This extends the work of López and Dahab, Okeya and Sakurai, and Brier and Joye to genus 2, and also to two-dimensional scalar multiplication. The technique is especially interesting in genus 2, because Kummer surfaces can outperform comparable elliptic curve systems.