MPC-in-the-Head Framework without Repetition and its Applications to the Lattice-based Cryptography

The MPC-in-the-Head framework has been proposed as a solution for Non-Interactive Zero-Knowledge Arguments of Knowledge (NIZKAoK) due to its efficient proof generation. However, most existing NIZKAoK constructions using this approach require multiple MPC evaluations to achieve negligible soundness error, resulting in proof size and time that are asymptotically at least λ times the size of the circuit of the NP relation. In this paper, we propose a novel method to eliminate the need for repeated MPC evaluations, resulting in a NIZKAoK protocol for any NP relation that we call Diet. The proof size and time of Diet are asymptotically only polylogarithmic with respect to the size of the circuit C of the NP relation, but are independent of the security parameter λ. Hence, both the proof size and time can be significantly reduced.Moreover, Diet offers promising concrete efficiency for proving Learning With Errors (LWE) problems and its variants. Our solution provides significant advantages over other schemes in terms of both proof size and proof time, when considering both factors together. Specifically, Diet is a promising method for proving knowledge of secret keys for lattice-based key encapsulation mechanisms (KEMs) such as Frodo and Kyber, offering a practical solution to future post-quantum certificate management. For Kyber 512, our implementation achieves an online proof size of 83.65 kilobytes (KB) with a preprocessing overhead of 152.02KB. The implementation is highly efficient, with an online proof time of only 0.68 seconds and a preprocessing time of 0.81 seconds. Notably, our approach provides the first reported implementation of proving knowledge of secret keys for Kyber 512 using post-quantum primitives-based zero-knowledge proofs.