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There are many results characterizing when derived categories of two complex surfaces are equivalent, including theorems of Bridgeland and Maciocia showing that derived equivalent Enriques or bielliptic surfaces must be isomorphic. The proofs of these theorems strongly use Torelli theorems and lattice-theo...
The proofs of Theorems 1 and 2 are reported in “Appendix” Sect. A. Theorem 1 can be used to prove the convergence of the elementary programs that specify matrix operations in Sect. 3.1 and the convergence of the WL algorithm that we shall see in Sect. 4.2. Theorem 2 ensures the conve...
Achieving malicious security requires to ensure correctness of computations which we obtain using simple zero-knowledge proofs of knowledge. Loosely speaking, the parties first generate a joint public key for the additive El Gamal PKE such that no party knows the secret key (this protocol is ...