Notes

• Multilinear polynomials are key components of the Sum-Check protocol in ZKP, used for efficient computation and verification
• Interpolation methods allow any function to be represented by multilinear polynomials on Boolean hypercubes, simplifying calculations
• Tensor product operations provide a vector space abstraction for polynomial multiplication, optimizing memory and time usage
• Coordinate calculations based on Lagrange basis, directly through function evaluation, improving efficiency
• These properties help accelerate Sum-Check proofs, reducing ZKP system overhead
• The article provides a mathematical foundation for understanding more complex ZKP protocols (e.g., GKR)

• 多线性多项式是ZKP中Sum-Check协议的关键组件，用于高效计算和验证
• 插值方法允许任意函数在布尔超立方体上被多线性多项式表示，简化计算
• 张量积操作提供多项式乘法的向量空间抽象，优化内存和时间使用
• 坐标计算基于拉格朗日基，直接通过函数求值获得，提升效率
• 这些性质有助于加速Sum-Check证明，减少ZKP系统的开销
• 文章为理解更复杂的ZKP协议（如GKR）提供了数学基础