Cycle of Curves

A cycle of curves involves using two different elliptic curves where the base field of one is the scalar field of the other. This mathematical relationship is essential for efficient recursive proof composition, as it allows a prover to verify a proof generated on a different curve without excessive computational overhead.

Without cycles of curves, recursive verification would be prohibitively expensive, requiring large field extensions that slow down the process. This enables the construction of efficient recursive SNARKs that can handle deep chains of logic.

In financial protocols, this provides the necessary performance to verify long chains of margin updates or complex order book states. It is a cornerstone of modern ZKP engineering.