Common use of Decomposability Clause in Contracts

Decomposability. The Aggregate algorithm can be decomposed into 2 algorithms Aggregate1 and Aggregate2, such that the following hold: • Aggregate1(pp, {vk1, . . . , vkn}, m, {σ1, . . . , σq}) → Ssig, where Ssig is of size poly(κ, log n). • Aggregate2(pp, m, Ssig) → σ, i.e., aggregate the signatures in Ssig into a new signature σ. A

Decomposability. The Aggregate algorithm can be decomposed into 2 algorithms Aggregate1 and Aggregate2, such that the following hold: • Aggregate1(pp, {vk1, . . . , vkn}, m, {σ1, . . . , σq}) → Ssig, where Ssig is of size poly(κ, log n). • Aggregate2(pp, m, Ssig) → σ, i.e., aggregate the signatures in Ssig into a new signature σ. A.

Decomposability. The Aggregate algorithm can be decomposed into 2 algorithms Aggregate1 and Aggregate2, such that the following hold: { } { } → • Aggregate1(pp, {vk1, . . . , vkn}vkn , m, {σ1, . . . , σq}σq ) → Ssig, where Ssig is of size poly(κpoly(log n, log n)) and Aggregate1 is deterministic. • Aggregate2(pp, m, Ssig) → σ, i.e., aggregate the signatures in Ssig into a new signature σ. A