當我們使用擴展因子 8 時，我們將在 p(x) 上計算另外 32 * (8-1) 個點。 由于兩個不同的 D 次多項式最多共享 D 個點，因此具有有效多項式 (滿足上述約束條件) 和 D 次假多項式 (不滿足上述約束條件) 的多項式對最多共享 D 個點。這意味著假多項式有 次機會通過隨機抽樣檢查。如果我們進行 n 次抽樣檢查，機會會降低到 。 我們默認將 extension_factor 設置為 16，將抽樣檢查默認次數設置為 16，因此安全級別將為 80 位。 第三步：多項式承諾 我們使用計算記錄和相應的用戶余額、用戶 ID 以及每行對應約束多項式的值來計算哈希值，并生成默克爾樹 (Mekel tree)。默克爾樹根是多項式的承諾 (commitment) 值。 第四步：生成抽樣證明 使用默克爾樹根作為隨機源對數據進行抽樣。為避免洩露計算記錄數據，在抽樣過程中將會避免使用序號為 *k ** extension_factor 的數據，并生成相應的默克爾證明路徑。 然後進行抽樣檢查，檢查承諾的多項式是否是滿足第一步中列出的約束條件的有效多項式。

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