Notes

• Lagrange interpolation generates the unique lowest degree polynomial through all given points
• Interpolation can be used for data recovery, such as audio data recovery
• In ZKP, polynomial interpolation supports efficient verification and comparison
• Schwartz-Zippel lemma allows verification of polynomials through a few points
• Lagrange method is simple and easy to understand, suitable for teaching and basic implementation
• In practical applications, other methods such as FFT may be more efficient

• Lagrange插值生成唯一最低次多项式通过所有给定点
• 插值可用于数据恢复，如音频丢失数据填补
• 在ZKP中，多项式插值支持高效验证和比较
• Schwartz-Zippel引理允许通过少数点验证多项式
• Lagrange方法简单易懂，适合教学和基础实现
• 实际应用中，FFT等其他方法可能更高效