[pbsd]

"Sequences of numbers generated by addition in formal groups and new primality and factorization tests", by the Chudnovsky brothers [1].

This paper is incredibly ahead of its time. While elliptic curves in cryptography are usually attributed to Hendrik Lenstra for destructive purposes (ECM factorization), and Koblitz and Miller for constructive purposes in 1985, this paper contains almost everything relevant to practical curve-based cryptography long before everyone else. Highlights include:

- Hessian, Jacobian quartic, and Jacobian intersection curves, and derivation of respective fast addition and doubling formulas; they also comment on the value of unified addition formulas for simplicity.

- The "Montgomery" ladder for "x-only" Jacobian intersections: Peter Montgomery was directly influenced by this paper to produce his curves, and it is easy to see the resemblance.

- The idea of working in genus 2, and formulas for genus 2 Kummer surface doubling. Hyperelliptic curve cryptography was only later proposed by Koblitz in 1987. Almost 3 decades later, Kummer surfaces are now the fastest way to do scalar multiplication on beefy hardware.

[1] http://www.sciencedirect.com/science/article/pii/01968858869...