Model-Generic Incrementally Verifiable Computation from Updatable BARGs

Abstract

Incrementally verifiable computation (IVC) is a computationally sound proof system that allows a prover to certify the correctness of a long or ongoing computation in an incremental manner, by repeatedly updating a proof certifying the computation so far. Updating the proof does not require access to the entire trace of the computation, which makes the IVC-prover memory efficient. Recently, such schemes were constructed for deterministic Turing machines from standard cryptographic assumptions (Paneth and Pass, FOCS 2022, and Devadas et al., FOCS 2022).
In this work we generalize and extend IVC to support incremental certification and verifiability of a large set of computation models, focusing on distributed and online computation. This allows distributed algorithms to efficiently certify their own execution using low memory and communication overhead. We construct IVC for a variety of computation models by proving one generic lifting theorem from a classical (non-incremental) delegation scheme (also known as SNARG) into full-fledged IVC, while preserving the delegation scheme’s succinctness properties (up to an additive factor which is polynomial in the security parameter and independent of the size of the computation). Using this lifting theorem, we obtain IVC for the following computation models:  
- RAM and exclusive-read exclusive-write (EREW) PRAM algorithms, using existing delegation schemes for these models. 
- Streaming algorithms, using the natural memory-efficiency properties of the model. 
- Massively parallel computation (MPC). Notably, in this model, memory efficiency is a critical bottleneck: the machines participating in an MPC algorithm usually cannot store the entire trace of their computation. Thus, certifying MPC algorithms naturally benefits from IVC. Moreover, since prior to our work, no delegation scheme for this model was known, we also construct a delegation scheme for one-round massively parallel computations, and then apply our lifting theorem to it. 
- Distributed graph algorithms, using existing distributed delegation schemes (also known as locally verifiable distributed SNARGs). Here, in order to use our lifting theorem we have to first make some observations about the verification procedure of these existing schemes. 

At the heart of this work is a new abstraction, updatable batch arguments for NP (UpBARGs), which we define and construct. Standard BARGs allow one to prove a batch of k NP-statements using a proof whose length barely grows with k; however, the statements and their witnesses must all be known in advance. In contrast, UpBARGs support adding statements and witnesses on the fly, making them a flexible tool for constructing IVC across different computational models.