我竟然会用readyu大侠的ECCTooL了

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技术分享 2月前 1 浏览

我竟然会用readyu大侠的ECCTooL了

我竟然会用readyu大侠的ECCTooL了
     看了一下readyu大侠的“椭圆曲线加密分析：FLEXLM ECC问答”这个酷帖，坦白的说，这不是科普文章。因我菜鸟我实在看不下去了，作者吐血给了工具，但偶竟然笨得不会用！(童鞋们会用的请举一下手啊，哇，这么多啊！买块豆腐撞死算了！)。没有说明书就不会用？这是理由吗？研究了约一个小时，终于有所心得。废话少说，开讲。

  只解释下面这段，原文如下：
   (1) 签名
   r = k * G mod n ... (1)  // 这里r应该是计算结果的横坐标吧？偶不懂
   s = (h + rd)/k mod n ... (2)
   (2) 验证(v == r)    //  这里应该是验证 V＝k * G mod n吧？
   u = h/s
    w = r/s
    V = u * G + w * R mod n
例子, NIST-P192 签名。
y^2 = x^3 - 3x + 64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1 mod FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF
n=FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831
取G(x,y):
Gx=188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012
Gy=07192B95FFC8DA78631011ED6B24CDD573F977A11E794811
取 d =16fdbb3f3e4d7d253c421ae5a09f1ce500d973c04ae91564
R(x,y) = d * G(x,y)=
Rx=2B443533CFBECB00ABE1F9D0F3A8FFD871EFDDAB4FF93B0C
Ry=6EFF3D69042B58F7C726BDB6B495AE75BD09D762259013DB
签名 "123"，即求sha1('123')，得到：
h = 40bd001563085fc35165329ea1ff5c5ecbdbbeef
取 k =CADDC27FEFC3040C1CCA194542218E002F58D504A639B668
Sign(用ECCTool计算):
sig.r=5C09A23549325C866F0C1D8D6AB81255977C90A9FD6D66C4
sig.s=C0DFFC8E4BA4A91EBFFBCE7FE07E202AAF567DC10D69D5E8
Verify (用ECCTool 和 BigIntCal计算):
u = h/s mod n = BBBBED787373E2407BA720D7851CE0895222B5B5DF81BECB
w = r/s mod n = 2BBC84EA2E318FC5666B50CEE41845F3EB1DF40C838FA86C
V(x,y) = u *G + w *R mod n =
V.x = 5C09A23549325C866F0C1D8D6AB81255977C90A9FD6D66C4
V.y = 70360EEEC1C42D5AC10226B8BE0EA507E3FF54290737B02C

下面使用作者的ecctool_v1.05，BigIntCalc_v1.14工具，给出原文数据来源。
已知条件：
A=-3
B=64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1
P=FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF
n=FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831
Rx=2B443533CFBECB00ABE1F9D0F3A8FFD871EFDDAB4FF93B0C
Ry=6EFF3D69042B58F7C726BDB6B495AE75BD09D762259013DB
Gx=188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012
Gy=07192B95FFC8DA78631011ED6B24CDD573F977A11E794811
h=40bd001563085fc35165329ea1ff5c5ecbdbbeef
r=5C09A23549325C866F0C1D8D6AB81255977C90A9FD6D66C4
d=16fdbb3f3e4d7d253c421ae5a09f1ce500d973c04ae91564
k=CADDC27FEFC3040C1CCA194542218E002F58D504A639B668
n=FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831
(1) 签名
   k * G mod n 的横坐标 r=5C09A23549325C866F0C1D8D6AB81255977C90A9FD6D66C4

   s= (h + rd)* k^-1   mod n
   h+rd=8440CC7A935B37A946574E1F0049F38B08062C127AA7F1E298C7EA7077ACDA445A513B5B8D54F1227DA37D6F469F77F
   h+rd mod n=4A36F71E1BE5CCC086A5483BAFF2F81F1B8729087731A60D
   k^-1  mod n= 3A5DF42EDE377F21CA637377C20FE43EDAFF70F0332641E1
   s= (4A36F71E1BE5CCC086A5483BAFF2F81F1B8729087731A60D * 3A5DF42EDE377F21CA637377C20FE43EDAFF70F0332641E1) mod n
    =10EBB0BE92170DD54EE7EBB5C4E4C549C785BC29C1303EC0EEC0E31E0EDE9703DC1604680CEBF5A83A5B28579ABA3E6D mod n
    =C0DFFC8E4BA4A91EBFFBCE7FE07E202AAF567DC10D69D5E8

  (2) 验证 V＝k * G mod n
    u = h/s mod n = BBBBED787373E2407BA720D7851CE0895222B5B5DF81BECB


   w = r/s mod n = 2BBC84EA2E318FC5666B50CEE41845F3EB1DF40C838FA86C

    V(x,y) = u *G + w *R mod n =
    V.x = 5C09A23549325C866F0C1D8D6AB81255977C90A9FD6D66C4
    V.y = 70360EEEC1C42D5AC10226B8BE0EA507E3FF54290737B02C

  与计算k * G mod n返回的结果比较，V.x和V.y显然与之相等，验证完毕。

                                                      天易love
                                                                               2012－08-19