International Association
for Cryptologic Research

Consider the task of secure multiparty computation (MPC) among n parties with perfect security and guaranteed output delivery, supporting t < n/3 active corruptions. Suppose the arithmetic circuit C to be computed is defined over a finite ring Z/qZ, for an arbitrary q ∈ Z. It is known that this type of MPC over such ring is possible, with communication that scales as O(n|C|), assuming that q scales as Ω(n). However, for constant-size rings Z/qZ where q = O(1), the communication is actually O(n log n|C|) due to the need of the so-called ring extensions. In most natural settings, the number of parties is variable but the “datatypes” used for the computation are fixed (e.g. 64-bit integers). In this regime, no protocol with linear communication exists. In this work we provide an MPC protocol in this setting: perfect security, G.O.D. and t < n/3 active corruptions, that enjoys linear communication O(n|C|), even for constant-size rings Z/qZ. This includes as important particular cases small fields such as F2, and also the ring Z/2k Z. The main difficulty in achieving this result is that widely used techniques such as linear secret-sharing cannot work over constant-size rings, and instead, one must make use of ring extensions that add Ω(log n) over- head, while packing Ω(log n) ring elements in each extension element in order to amortize this cost. We make use reverse multiplication-friendly embeddings (RMFEs) for this packing, and adapt recent techniques in network routing (Goyal et al. CRYPTO’22) to ensure this can be efficiently used for non-SIMD circuits. Unfortunately, doing this naively results in a restriction on the minimum width of the circuit, which leads to an extra additive term in communication of poly(n) · depth(C). One of our biggest technical contributions lies in designing novel techniques to overcome this limitation by packing elements that are distributed across different layers. To the best of our knowledge, all works that have a notion of packing (e.g. RMFE or packed secret-sharing) group gates across the same layer, and not doing so, as in our work, leads to a unique set of challenges and complications.

Software Guard Extension (SGX) is a hardware-based trusted execution environment (TEE) implemented in recent Intel commodity processors. By isolating the memory of security-critical applications from untrusted software, this mechanism provides users with a strongly shielded environment called enclave for executing programs safely. However, recent studies have demonstrated that SGX enclaves are vulnerable to side-channel attacks. In order to deal with these attacks, several protection techniques have been studied and utilized.In this paper, we explore a new pattern history table (PHT) based side-channel attack against SGX named Bluethunder, which can bypass existing protection techniques and reveal the secret information inside an enclave. Comparing to existing PHT-based attacks (such as Branchscope [ERAG+18]), Bluethunder abuses the 2-level directional predictor in the branch prediction unit, on top of which we develop an exploitation methodology to disclose the input-dependent control flow in an enclave. Since the cost of training the 2-level predictor is pretty low, Bluethunder can achieve a high bandwidth during the attack. We evaluate our attacks on two case studies: extracting the format string information in the vfprintf function in the Intel SGX SDK and attacking the implementation of RSA decryption algorithm in mbed TLS. Both attacks show that Bluethunder can recover fine-grained information inside an enclave with low training overhead, which outperforms the latest PHT-based side channel attack (Branchscope) by 52×. Specifically, in the second attack, Bluethunder can recover the RSA private key with 96.76% accuracy in a single run.