Most existing work on secure multi-party computation (MPC) ignores a key idiosyncrasy of modern communication networks, that there are a limited number of communication paths between any two nodes, many of which might even be corrupted. The problem becomes particularly acute in the information-theoretic setting, where the lack of trusted setups (and the cryptographic primitives they enable) makes communication over sparse networks more challenging. The work by Garay and Ostrovsky [EUROCRYPT’08] on almost-everywhere MPC (AE-MPC), introduced “best-possible security” properties for MPC over such incomplete networks, where necessarily some of the honest parties may be excluded from the computation. In this work, we provide a universally composable definition of almost-everywhere security , which allows us to automatically and accurately capture the guarantees of AE-MPC (as well as AE-communication, the analogous “best-possible security” version of secure communication) in the Universal Composability (UC) framework of Canetti. Our results offer the first simulation-based treatment of this important but under-investigated problem, along with the first simulation-based proof of AE-MPC. To achieve that goal, we state and prove a general composition theorem, which makes precise the level or “quality” of AE-security that is obtained when a protocol’s hybrids are replaced with almost-everywhere components.

Code‐based digital signatures suffer from two main drawbacks: large public key size and slow signature generation. Large public key size is inherent in almost all the code‐based cryptosystems and other post‐quantum alternatives; however, slow signature generation is due to their specific structure. Most of the current code‐based signature schemes are constructed based on Courtois, Finiasz, and Sendrier (CFS) signature. CFS uses a counter to produce decodable syndromes or the complete decoding technique that imposes some extra computational cost to the signing algorithm for many choices of codes. In this study, the authors propose an efficient digital signature, PolarSig, which can reduce both public key size and signing time simultaneously. PolarSig uses some specific instances of polar codes that enable us to decode every random syndrome. Moreover, they apply puncturing and randomised omitting of frozen bits to protect the authors’ scheme from commonplace attacks targeting former cryptosystems based on polar codes. Besides, they prove that their signature is existentially unforgeable under a chosen message attack secure in the random oracle model.