Common use of Average-Case Soundness Clause in Contracts

Average-Case Soundness. For any non-uniform PPT prover P∗, it holds that Pr [S.Verify(crs, x, π) = 1 | crs ← S.Setup(1κ, 1n), x ← Dno(1n), π ← P∗(crs, x)] ≤ negl(n, κ). SRDS based on multi-signatures. We consider implications of SRDS constructions based on an underlying multi-signature scheme (see Appendix A.3) in the following sense. While rigorously specifying the notion is rather involved, at a high level, such a scheme is one that satisfies three natural properties:

Average-Case Soundness. For any non-uniform PPT prover P∗, it holds that Pr [S.Verify(crs, x, π) = 1 | crs ← S.Setup(1κ, 1n), x ← Dno(1n), π ← P∗(crs, x)] ≤ negl(n, κ). SRDS based on multi-signatures. We consider implications of SRDS constructions based on an underlying multi-signature scheme (see Appendix A.3) in the following sense. While rigorously specifying the notion is rather involved, at a high level, such a scheme is one that satisfies satisfies three natural properties:

Average-Case Soundness. For any non-uniform PPT prover P∗, it holds that Pr [S.Verify(crs, x, π) = 1 | crs ← S.Setup(1κS.Setup(1n, 1n), x ← Dno(1n), π ← P∗(crs, x)] ≤ negl(n, κn). SRDS based on multi-signatures. We consider implications of SRDS constructions based on an underlying multi-signature scheme (see Appendix A.3A.4) in the following sense. While rigorously specifying the notion is rather involved, at a high level, such a scheme is one that satisfies three natural properties: