Research on Secure Multi-Party Computation (SMPC) has been ongoing for over 40 years. With the rise of Zero-Knowledge (ZK) technology, more studies and applications are emerging. This blog aims to explore the potential effects of SMPC on Relinx.
Understanding SMPC
SMPC can be simplified as follows: multiple parties jointly perform a computation, but each party can only see its own input and output. However, any party can verify the correctness of the public output. This can be represented as f(x₁, x₂, ... , xₙ) = (y₁, y₂,...,yₙ), where each party Pᵢ knows its own xᵢ and computes yᵢ. Honest parties will obtain the same yᵢ. Let's delve into some concrete examples to better understand this abstract concept.
Common Applications: Threshold Signature Schemes (TSS)
One common application is Threshold Signature Schemes (TSS), widely used in scenarios requiring t/n multi-signature schemes. Each party holds a private key, and when more than t parties sign, a public signature can be computed and verified by anyone. For example, in the Discrete Logarithm Key Generation (DKG) process, each participant Pᵢ samples t random values (aᵢ₀, ..., aᵢ₍ₜ₋₁₎) ← ℤ and uses them to define a degree t−1 polynomial fᵢ(x)=Σⱼaᵢⱼxʲ. Pᵢ computes a proof of knowledge of the corresponding secret aᵢ₀ by calculating and broadcasting (Cᵢ,Rᵢ,μᵢ), where Rᵢ=gᵏ, k←ℤ and μᵢ=k+aᵢ₀⋅H(i,Φ,Aᵢ₀,Rᵢ). Each participant then sends (j,fᵢ(j)) to others, and every participant calculates their secret input sᵢ=Σⱼfⱼ(i). Any participant can compute the public key Sᵢ=ΠⱼⁿΠₖᵗ⁻¹(Aⱼₖ^(iᵏ mod q)), and the common public key is S=ΠⱼAⱼ₀. After completing DKG, efficient t/n multi-signatures can be achieved, which is also an instance of MPC.
General Frameworks Based on Garbled Circuits
Over the years, many general frameworks based on Garbled Circuits have been developed and practiced. A simple two-party computation framework can be described as follows: Two computing parties, Alice and Bob, jointly compute f(s,t), where s is Alice's input, t is Bob's input, and f is the computing logic. Alice first converts f into a Boolean circuit C, with a truth table for each gate. Alice then encrypts the truth table to get the garbled circuit 𝒞, encrypts her input, and sends the encrypted input and 𝒞 to Bob. Bob obtains 𝒞 and Alice's encrypted input but cannot obtain his own encrypted input without knowing Alice's encryption. Bob then performs a 1-out-of-2 OT with Alice to get his input label. Finally, Bob decrypts the garbled circuit using both parties' encrypted inputs and obtains the result.
Extending to Multiple Parties: BMR Protocol
The basic BMR idea is to perform distributed GC generation so that no single party or a proper subset of parties knows the GC generation secrets — the label assignment and correspondence. This can be done in parallel for all gates using MPC by first generating all wire labels independently and then independently generating garbled gate tables.
Applying These Technologies in Relinx
Relinx utilizes these technologies in its Universal Consensus Layer, built on SMPC. A decentralized key agreement forms an MPC network, which then achieves consensus on transactions or data within the network. An aggregate signature is formed during the consensus process, and when it is verified, the network is considered to have reached consensus.
The specific consensus algorithm can be implemented via the Modular Consensus Service. This can be a traditional program module run in a secure sandbox or a blinded circuit algorithm to better protect computational privacy. Additionally, we are closely monitoring the progress of zkVM to further enhance performance and privacy protection through zkProof.
In conclusion, SMPC and related technologies have vast potential and are actively being integrated into platforms like Relinx to provide secure, private, and efficient computational solutions.
