We survey several security assumptions based on physical principles as opposed to more common complexity-theoretic assumptions. This survey focuses on obtaining security guarantees via i) idealized hardware and ii) physical objects, and specifies how these assumptions have been used for devising cryptographic protocols, such as protocols for secure multi-party computation. Note that due to these assumptions, the protocols are often conceptually simpler, the security is independent of the computational power of an attacker, and the functioning and security is more transparent to humans.

Abstract In practice, there are numerous settings where mutually distrusting parties need to perform distributed computations on their private inputs. For instance, participants in a first-price sealed-bid online auction do not want their bids to be disclosed. This problem can be addressed using secure multi-party computation (MPC), where parties can evaluate a publicly known function on their private inputs by executing a specific protocol that only reveals the correct output, but nothing else about the private inputs. Such distributed computations performed over the Internet are susceptible to remote hacks that may take place during the computation. As a consequence, sensitive data such as private bids may leak. All existing MPC protocols do not provide any protection against the consequences of such remote hacks. We present the first MPC protocols that protect the remotely hacked parties’ inputs and outputs from leaking. More specifically, unless the remote hack takes place before the party received its input or all parties are corrupted, a hacker is unable to learn the parties’ inputs and outputs, and is also unable to modify them. We achieve these strong (privacy) guarantees by utilizing the fact that in practice parties may not be susceptible to remote attacks at every point in time, but only while they are online, i.e. able to receive messages. To this end, we model communication via explicit channels. In particular, we introduce channels with an airgap switch (disconnect-able by the party in control of the switch), and unidirectional data diodes. These channels and their isolation properties, together with very few, similarly simple and plausibly remotely unhackable hardware modules serve as the main ingredient for attaining such strong security guarantees. In order to formalize these strong guarantees, we propose the UC with Fortified Security (UC#) framework, a variant of the Universal Composability (UC) framework.

Abstract A private stream aggregation (PSA) scheme is a protocol of n clients and one aggregator. At every time step, the clients send an encrypted value to the (untrusted) aggregator, who is able to compute the sum of all client values, but cannot learn the values of individual clients. One possible application of PSA is privacy-preserving smart-metering, where a power supplier can learn the total power consumption, but not the consumption of individual households. We construct a simple PSA scheme that supports labels and which we prove to be secure in the standard model. Labels are useful to restrict the access of the aggregator, because it prevents the aggregator from combining ciphertexts with different labels (or from different time-steps) and thus avoids leaking information about values of individual clients. The scheme is based on key-homomorphic pseudorandom functions (PRFs) as the only primitive, supports a large message space, scales well for a large number of users and has small ciphertexts. We provide an implementation of the scheme with a lattice-based key-homomorphic PRF (secure in the ROM) and measure the performance of the implementation. Furthermore, we discuss practical issues such as how to avoid a trusted party during the setup and how to cope with clients joining or leaving the system.