标题： 树和公式的多项式指纹识别 显示英文标题

标题： Polynomial fingerprinting for trees and formulas

摘要： 为了满足（零知识）证明对于（数学）证明的需求，我们描述了一种方法，将多元整系数多项式上的2x2矩阵中的形式句子进行转换，使得通常的证明步骤如假言推理或替换很容易从作为参数使用的项或公式的矩阵中计算得出。 通过在适当选择的有限域的随机元素中对多项式变量进行求值，证明被替换为一个数字序列。 只有对应于公理的值需要从头计算。 对应于推导出的公式的值是通过应用同态性质，从其祖先对应的值计算得出的。 在这样的序列上，可以应用各种零知识方法。 显示英文摘要

摘要： To cater to the needs of (Zero Knowledge) proofs for (mathematical) proofs, we describe a method to transform formal sentences in 2x2 - matrices over multivariate polynomials with integer coefficients, such that usual proof-steps like modus-ponens or the substitution are easy to compute from the matrices corresponding to the terms or formulas used as arguments. By evaluating the polynomial variables in random elements of a suitably chosen finite field, the proof is replaced by a numeric sequence. Only the values corresponding to the axioms have to be computed from scratch. The values corresponding to derived formulas are computed from the values corresponding to their ancestors by applying the homomorphic properties. On such sequences, various Zero Knowledge methods can be applied.