I don't get this article. They make a big fuss about looking for the right category, because apparently the category of groups cannot explain the difficulty of breaking Diffie-Hellman, since there is an isomorphism <g> -> Z/nZ. But the same isomorphism exists in the category of algebraic varieties! So was all in vain?
To me this sounds a bit like an a-posteriori justification of why people use elliptic curves to do cryptography. This feels weird to me, as elliptic curves are a well-studied subject in algebraic geometry, whose history reaches back over 150 years to Clebsch. So when Victor Miller and Neal Koblitz proposed to do cryptography with them, they already knew very well about elliptic curves (both have a background in algebraic geometry of finite fields).
To me this sounds a bit like an a-posteriori justification of why people use elliptic curves to do cryptography. This feels weird to me, as elliptic curves are a well-studied subject in algebraic geometry, whose history reaches back over 150 years to Clebsch. So when Victor Miller and Neal Koblitz proposed to do cryptography with them, they already knew very well about elliptic curves (both have a background in algebraic geometry of finite fields).