3 ms·
Not really, assuming you mean "continuous" by "analog". ECC relies on the existence of an elliptic curve group to be reversible. Groups are inherently discrete
by SAI_Peregrinus 5y ago
Not really, assuming you mean "continuous" by "analog". ECC relies on the existence of an elliptic curve group to be reversible. Groups are inherently discrete structures, I'm not aware of any continuous structures with similarly useful properties.
- joppy 5y agoGroups are not inherently discrete - there are many continuous groups (called Lie groups) such as the circle, group of rotations in 3D, etc etc. You can also see this turn up in Fourier theory: the discrete Fourier transform has an underlying discrete group, Fourier series for a periodic function are really using the circle group underneath, and the Fourier transform on the real line is using the continuous group of the real line, with addition as the group operation. Elliptic curves are nice because they are algebraic groups, so by plugging in complex or real numbers you get a continuous group, and by plugging in finite fields you get a discrete group.