Feistel Structures for MPC, and More

Privacy Preserving CTL Model Checking through Oblivious Graph Algorithms

“…As such, the probability must be the same for all indices. Then, as before by (1) and the law of total probability we have Pr[i * (t ) = i = α] = 1/(n − t − 1). □…”

“…Recent work on developing more efficient PRFs for use within MPC has produced primitives with an order of magnitude better performance than AES [1][2][3]30]. In addition, some of these primitives are naturally computed in arithmetic circuits, which may provide a more efficient setting for some of the other intermediary computations we require.…”

“…by outputting a bit b ∈ {0, 1} identifying which counterparty they are interacting with. We will define secure computation of a function f : 1 Also known as the honest-but-curious model. computationally indistinguishable, or…”

“…In addition to generic MPC tools and techniques, our protocol is particularly dependent on both the in-circuit PRF and oblivious graph algorithms. Constructing PRFs specifically for multiparty computation is an active area of research, providing promising schemes which may dramatically reduce the concrete overhead of our protocol [1][2][3]30]. Data-oblivious graph algorithms have also received attention both generically and within a variety of problem domains [10,11,22,27,28,56].…”

An Algebraic Attack on Ciphers with Low-Degree Round Functions: Application to Full MiMC

“…For example, we can consider the substitution (S-box) layer, that is, the operation providing nonlinearity in the permutation: In these new schemes, the S-boxes composing this layer are relatively large compared to the ones used in classical schemes (e.g., they operate over 64 or 128 bits instead of 4 or 8 bits) and/or they can usually be described by a simple low-degree nonlinear function (e.g., x → x d for some d). Examples of these schemes include LowMC [5], MiMC [4], Jarvis/Friday [7], GMiMC [3], HadesMiMC [33], Vision/Rescue [6], and Starkad/Poseidon [32].…”