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BLS signature

BLS signature. G 1 ,G 2 and G T 是 ( 乘法 ) 循環群 , 屬於指令 P g1 ← G1 ； g2 ←G2 g 1 產生於 G 1 g 2 產生於 G 2 Ψ 是一 可計算的同構從 G 2 到 G 1 , 用 Ψ ( g 2 ) = g 1 e 是一 可計算的雙線性映射 e : G 1 × G 2 → G T. co-CDH, co-DDH and co-GDH problems. 計算 co-Diffie-Hellman (co-CDH) on (G 1 ,G 2 ):

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BLS signature

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  1. BLS signature

  2. G1,G2 and GT 是(乘法)循環群,屬於指令P • g1 ← G1 ； g2 ←G2 • g1產生於G1 • g2 產生於G2 • Ψ是一可計算的同構從G2到 G1 , 用Ψ(g2) = g1 • e是一可計算的雙線性映射 e : G1 × G2 →GT

  3. co-CDH, co-DDH and co-GDH problems 計算 co-Diffie-Hellman (co-CDH) on (G1,G2): 假設 g2,g2a∈G2 and h ∈ G1, 計算 ha∈ G1. 決定 co-Diffie-Hellman (co-DDH) on (G1,G2): 假設 g2,g2a∈ G2 and h,hb∈ G1, Output YES if a = b and Output no otherwise

  4. 一個成功概率算法 A 在解決 co-CDH problem on (G1, G2) • 兩組(G1, G2)是一(τ, t,ε)-co-GDH group pair : • - 在兩組群運算G1 and G2 and the map ψ可 以計算在大部分時間τ • - co-DDH問題在(G1, G2)可以解決大部分的時間τ • 沒有算法 (t,ε)-breaks co-CDH on (G1, G2)

  5. 當(G1, G1)是一 (τ, t, ε)-co-GDH group pair 我們說 G1是一 (τ, t, ε)-GDH group • 雙線性映射

  6. 短簽名方案 • 允許(G1, G2)是(t,ε)-co-GDH 組對 • |G1| = |G2| = p • 哈希函數H: {0, 1}∗ → G1 • 簽字σ是 一個屬於G1的要素 • 該簽名方案包含三個運算法則，密碼生成，簽名和驗證

  7. 密碼生成: • 私鑰 • 公鑰 • 簽名: • 驗證:

  8. 安全 • 安全簽名計劃相對存在偽造在適應性選擇，消息攻擊下在隨機預言模型 • 存在偽造 • -創造（尤對手）任何信息m和一有效的簽名σ為m,其中m尚未簽署 • -該消息m不必有任何特殊的含義,只要這一對(m,σ) 是有效的,敵手已經成功地構建一個存在偽造 • -存在偽造是實質上那些最弱的敵對目標,因此，最強烈的那些計劃“其存在是不可偽造的”

  9. 適應的選擇,訊息攻擊 • -攻擊模型為了數位簽名 • -攻擊者可以要求一預言式簽名簽署任意訊息 • -他可以這樣做多次和適應他所選擇的基礎,這個結果屬於前面的簽名查詢 • -攻擊被認為是成功的,如果攻擊者可以想出一個簽名的訊息為此他以前沒有要求簽名

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