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抛币协议

1. 使用单向函数

  1. Alice和Bob各自选择一个随机字符串，比如"ljngjkrjgnfdudiudd" 和 "gfdgdfjkherfsfsd"
  2. Alice随机生成一个抛硬币的结果，比如"tail"
  3. Bob把自己的随机字符串发送给Alice
  4. Alice把抛币结果和两个人的随机字符串合并成一个新的字符串，例如"tail ljngjkrjgnfdudiudd gfdgdfjkherfsfsd"，并且把这个字符串的hash值"59dea408d43183a3937957e71a4bcacc616d9cbc"发送给Bob
  5. Alice问Bob: “你猜是head还是tail"?
  6. Bob猜一个结果，比如"head"
  7. Alice告诉告诉Bob他猜错了，并且出示完整的字符串

2. 使用满足交换律的加密算法

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满足")),Q("mjx-container",d,[(l(),t("svg",r,T[2]||(T[2]=[m('',1)]))),T[3]||(T[3]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"e"),Q("mi",null,"a")]),Q("msub",null,[Q("mi",null,"d"),Q("mi",null,"a")]),Q("mo",null,"≡"),Q("msub",null,[Q("mi",null,"e"),Q("mi",null,"b")]),Q("msub",null,[Q("mi",null,"d"),Q("mi",null,"b")]),Q("mo",null,"≡"),Q("mn",null,"1"),Q("mspace",{width:"0.444em"}),Q("mo",{stretchy:"false"},"("),Q("mi",null,"mod"),Q("mspace",{width:"0.333em"}),Q("mi",null,"ϕ"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"p"),Q("mi",null,"q"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1))])]),Q("li",null,[T[10]||(T[10]=a("Alice生成两份消息")),Q("mjx-container",i,[(l(),t("svg",g,T[6]||(T[6]=[m('',1)]))),T[7]||(T[7]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"M"),Q("mn",null,"1")])])],-1))]),T[11]||(T[11]=a("和")),Q("mjx-container",h,[(l(),t("svg",H,T[8]||(T[8]=[m('',1)]))),T[9]||(T[9]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"M"),Q("mn",null,"2")])])],-1))]),T[12]||(T[12]=a('，一份表示"head"，一份表示"tail"，这些字符串还要包含双方协商好的特定字符串和随机字符串，以满足后期的验证'))]),Q("li",null,[T[15]||(T[15]=a("Alice使用自己的公钥加密这两份消息，得到")),Q("mjx-container",p,[(l(),t("svg",L,T[13]||(T[13]=[m('',1)]))),T[14]||(T[14]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"E"),Q("mi",null,"a")]),Q("mo",{stretchy:"false"},"("),Q("msub",null,[Q("mi",null,"M"),Q("mn",null,"1")]),Q("mo",{stretchy:"false"},")"),Q("mo",null,","),Q("msub",null,[Q("mi",null,"E"),Q("mi",null,"a")]),Q("mo",{stretchy:"false"},"("),Q("msub",null,[Q("mi",null,"M"),Q("mn",null,"2")]),Q("mo",{stretchy:"false"},")")])],-1))]),T[16]||(T[16]=a("，并且以随机的顺序发给Bob"))]),Q("li",null,[T[21]||(T[21]=a("Bob无法识别消息的内容，随机选择其中的一个消息")),Q("mjx-container",u,[(l(),t("svg",M,T[17]||(T[17]=[Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D440",d:"M289 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使用二次剩余")])],-1)),Q("ol",null,[Q("li",null,[T[39]||(T[39]=a("Alice选择两个质数")),Q("mjx-container",v,[(l(),t("svg",y,T[33]||(T[33]=[m('',1)]))),T[34]||(T[34]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"p"),Q("mo",null,","),Q("mi",null,"q")])],-1))]),T[40]||(T[40]=a("，计算")),Q("mjx-container",b,[(l(),t("svg",D,T[35]||(T[35]=[m('',1)]))),T[36]||(T[36]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"q"),Q("mi",null,"p")])],-1))]),T[41]||(T[41]=a("，然后将")),Q("mjx-container",j,[(l(),t("svg",C,T[37]||(T[37]=[Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 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