1. A computer-implemented method comprising: generating a Shafarevich-Tate group from an abelian variety; determining a Cassels-Tate pairing based on elements of the Shafarevich-Tate group; and cryptographically processing data based on the Cassels-Tate pairing by hashing the data into an element of the Shafarevich-Tate group using Kolyvagin cohomology classes.