In this article, we explore a novel approach to compressing MIP∗ protocols, which are widely used in various cryptographic applications. The proposed method, called swer reduction, significantly reduces the size of these protocols without compromising their security.
To understand how swer reduction works, let’s first define what MIP∗ protocols are. They are a type of cryptographic protocol that consists of multiple layers of codes, each designed to provide specific security features. The most common technique used in MIP∗ protocols is answer reduction, which helps reduce the size of the code by combining multiple bits of a codeword at the same time.
Our approach involves applying two rounds of answer reduction: first with the low-degree code and then with the Hadamard code. By concatenating these codes, we can achieve a significant reduction in the size of the MIP∗ protocol without compromising its security. We demonstrate that this method is more efficient than previous approaches while being simpler to analyze.
To put it simply, swer reduction is like a two-stage compression system for MIP∗ protocols. The first stage uses answer reduction to combine multiple bits of a codeword, similar to how you might bundle multiple items together in a shopping bag. The second stage uses the low-degree code and Hadamard code to further compress the bundle, much like how you might use different types of packing materials to maximize space efficiency in a suitcase.
The key advantage of swer reduction is that it allows for a more efficient compression of MIP∗ protocols without compromising their security. This makes them more practical for various cryptographic applications, such as secure messaging or digital signatures. Additionally, our approach is simpler to analyze and implement than previous methods, making it a promising solution for the future of cryptography.
Nondeterministic Algorithm for Noisy Nonlocal Games with Noisy MESs
