Cryptographic MPC Protocols

Ioan Ionescu, Ruxandra F. Olimid

The paper presents an analysis of Commitment Schemes (CSs) used in Multi-Party Computation (MPC) protocols. While the individual properties of CSs and the guarantees offered by MPC have been widely studied in isolation, their interrelation in concrete protocols and applications remains mostly underexplored. This paper presents the relation between the two, with an emphasis on (security) properties and their impact on the upper layer MPC. In particular, we investigate how different types of CSs contribute to various MPC constructions and their relation to real-life applications of MPC. The paper can also serve as a tutorial for understanding the cryptographic interplay between CS and MPC, making it accessible to both researchers and practitioners. Our findings emphasize the importance of carefully selecting CS to meet the adversarial and functional requirements of MPC, thereby aiming for more robust and privacy-preserving cryptographic applications.

Hans Delfs, Helmut Knebl

Akshayaram Srinivasan

Secure Multiparty Computation (MPC) allows a set of parties, each having its own private data, to compute a function of their joint data such that the parties only learn the output of this function and everything else about their data is hidden. MPC is a fundamental cryptographic abstraction that captures many other natural cryptographic primitives as special cases. It also has a wide range of practical applications such as conducting secure electronic auctions, delegating sensitive computation to untrusted cloud service providers, secure computation on genomic data and training machine learning models on private data.A long-standing open problem in this area is to construct MPC protocols that have {\\it optimal} (two-round) round complexity under the {\\it weakest} possible cryptographic hardness assumptions.We {\\it completely resolve} this problem by showing lower bounds and matching upper bounds on the hardness assumptions required for constructing round-optimal MPC. Specifically, we obtain the following results.\\begin{itemize}\\item \\textbf{Black-Box Separation.} We show that there exists no construction of two-round semi-honest MPC protocol for general functions that makes black-box use of a two-round oblivious transfer. As a corollary, a similar separation holds when starting with any 2-party functionality other than oblivious transfer. \\item \\textbf{Non-Black-Box Construction.} We show that the above negative result can be bypassed by making non-black-box use of a two-round oblivious transfer. Specifically, starting from a semi-honest (resp. malicious) secure two-round oblivious transfer protocol, we construct a two-round MPC protocol against semi-honest (resp. malicious) adversaries. \\end{itemize}Since any two-round MPC protocol for general functionalities implies a two-round oblivious transfer as a special case, the above two results show that non-black-box use of oblivious transfer is {\\it necessary and sufficient} to construct round-optimal MPC protocols.

Hikaru Tsuchida, Takashi Nishide

Multiparty computation (MPC) is a cryptographic method that enables a set of parties to compute an arbitrary joint function of the private inputs of all parties and does not reveal any information other than the output. MPC based on a secret sharing scheme (SS-MPC) and garbled circuit (GC) is known as the most common MPC schemes. Another cryptographic method, homomorphic encryption (HE), computes an arbitrary function represented as a circuit by using ciphertexts without decrypting them. These technologies are in a trade-off relationship for the communication/round complexities, and the computation cost. The private decision tree evaluation (PDTE) is one of the key applications of these technologies. There exist several constant-round PDTE protocols based on GC, HE, or the hybrid schemes that are secure even if a malicious adversary who can deviate from protocol specifications corrupts some parties. There also exist other protocols based only on SS-MPC that are secure only if a semi-honest adversary who follows the protocol specification corrupts some parties. However, to the best of our knowledge, there are currently no constant-round PDTE protocols based only on SS-MPC that are secure against a malicious adversary. In this work, we propose a constant-round four-party PDTE protocol that achieves malicious security. Our protocol provides the PDTE securely and efficiently even when the communication environment has a large latency.

Hans Delfs, Helmut Knebl