小尾数为整数（或BigInteger的）

我不知道是否有到numbers that are in little endians到的BigInteger或长转换在python和Java的方式。他们是in little endians format。这些数字采用C结构格式，它们不仅仅是十六进制，所以它很混乱。小尾数为整数（或BigInteger的）

/* This is free and unencumbered software released into the public domain. 
* 
* Anyone is free to copy, modify, publish, use, compile, sell, or 
* distribute this software, either in source code form or as a compiled 
* binary, for any purpose, commercial or non-commercial, and by any 
* means. 
* 
* See LICENSE for complete information. 
*/ 

static uint64_t rlwe_table[52][3] = { 
    {0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x1FFFFFFFFFFFFFFF}, 
    {0xE0C81DA0D6A8BD22, 0x161ABD186DA13542, 0x5CEF2C248806C827}, 
    {0x8D026C4E14BC7408, 0x4344C125B3533F22, 0x9186506BCC065F20}, 
    {0x10AC7CEC7D7E2A3B, 0x5D62CE65E6217813, 0xBAAB5F82BCDB43B3}, 
    {0x709C92996E94D801, 0x1411F551608E4D22, 0xD7D9769FAD23BCB1}, 
    {0x6287D827008404B7, 0x7E1526D618902F20, 0xEA9BE2F4D6DDB5ED}, 
    {0x34CBDC118C15F40E, 0xE7D2A13787E94674, 0xF58A99474919B8C9}, 
    {0xD521F7EBBBE8C3A2, 0xE8A773D9A1EA0AAB, 0xFB5117812753B7B8}, 
    {0xC3D9E58131089A6A, 0x148CB49FF716491B, 0xFE151BD0928596D3}, 
    {0x2E060C4A842A27F6, 0x07E44D009ADB0049, 0xFF487508BA9F7208}, 
    {0xFCEDEFCFAA887582, 0x1A5409BF5D4B039E, 0xFFC16686270CFC82}, 
    {0x4FE22E5DF9FAAC20, 0xFDC99BFE0F991958, 0xFFEC8AC3C159431B}, 
    {0xA36605F81B14FEDF, 0xA6FCD4C13F4AFCE0, 0xFFFA7DF4B6E92C28}, 
    {0x9D1FDCFF97BBC957, 0x4B869C6286ED0BB5, 0xFFFE94BB4554B5AC}, 
    {0x6B3EEBA74AAD104B, 0xEC72329E974D63C7, 0xFFFFAADE1B1CAA95}, 
    {0x48C8DA4009C10760, 0x337F6316C1FF0A59, 0xFFFFEDDC1C6436DC}, 
    {0x84480A71312F35E7, 0xD95E7B2CD6933C97, 0xFFFFFC7C9DC2569A}, 
    {0x23C01DAC1513FA0F, 0x8E0B132AE72F729F, 0xFFFFFF61BC337FED}, 
    {0x90C89D6570165907, 0x05B9D725AAEA5CAD, 0xFFFFFFE6B3CF05F7}, 
    {0x692E2A94C500EC7D, 0x99E8F72C370F27A6, 0xFFFFFFFC53EA610E}, 
    {0x28C2998CEAE37CC8, 0xC6E2F0D7CAFA9AB8, 0xFFFFFFFF841943DE}, 
    {0xC515CF4CB0130256, 0x4745913CB4F9E4DD, 0xFFFFFFFFF12D07EC}, 
    {0x39F0ECEA047D6E3A, 0xEE62D42142AC6544, 0xFFFFFFFFFE63E348}, 
    {0xDF11BB25B50462D6, 0x064A0C6CC136E943, 0xFFFFFFFFFFD762C7}, 
    {0xCDBA0DD69FD2EA0F, 0xC672F3A74DB0F175, 0xFFFFFFFFFFFC5E37}, 
    {0xFDB966A75F3604D9, 0x6ABEF8B144723D83, 0xFFFFFFFFFFFFB48F}, 
    {0x3C4FECBB600740D1, 0x697598CEADD71A15, 0xFFFFFFFFFFFFFA72}, 
    {0x1574CC916D60E673, 0x12F5A30DD99D7051, 0xFFFFFFFFFFFFFFA1}, 
    {0xDD3DCD1B9CB7321D, 0x4016ED3E05883572, 0xFFFFFFFFFFFFFFFA}, 
    {0xB4A4E8CF3DF79A7A, 0xAF22D9AFAD5A73CF, 0xFFFFFFFFFFFFFFFF}, 
    {0x91056A8196F74466, 0xFBF88681905332BA, 0xFFFFFFFFFFFFFFFF}, 
    {0x965B9ED9BD366C04, 0xFFD16385AF29A51F, 0xFFFFFFFFFFFFFFFF}, 
    {0xF05F75D38F2D28A3, 0xFFFE16FF8EA2B60C, 0xFFFFFFFFFFFFFFFF}, 
    {0x77E35C8980421EE8, 0xFFFFEDD3C9DDC7E8, 0xFFFFFFFFFFFFFFFF}, 
    {0x92783617956F140A, 0xFFFFFF63392B6E8F, 0xFFFFFFFFFFFFFFFF}, 
    {0xA536DC994639AD78, 0xFFFFFFFB3592B3D1, 0xFFFFFFFFFFFFFFFF}, 
    {0x8F3A871874DD9FD5, 0xFFFFFFFFDE04A5BB, 0xFFFFFFFFFFFFFFFF}, 
    {0x310DE3650170B717, 0xFFFFFFFFFF257152, 0xFFFFFFFFFFFFFFFF}, 
    {0x1F21A853A422F8CC, 0xFFFFFFFFFFFB057B, 0xFFFFFFFFFFFFFFFF}, 
    {0x3CA9D5C6DB4EE2BA, 0xFFFFFFFFFFFFE5AD, 0xFFFFFFFFFFFFFFFF}, 
    {0xCFD9CE958E59869C, 0xFFFFFFFFFFFFFF81, 0xFFFFFFFFFFFFFFFF}, 
    {0xDB8E1F91D955C452, 0xFFFFFFFFFFFFFFFD, 0xFFFFFFFFFFFFFFFF}, 
    {0xF78EE3A8E99E08C3, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, 
    {0xFFE1D7858BABDA25, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, 
    {0xFFFF9E52E32CAB4A, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, 
    {0xFFFFFEE13217574F, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, 
    {0xFFFFFFFD04888041, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, 
    {0xFFFFFFFFF8CD8A56, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, 
    {0xFFFFFFFFFFF04111, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, 
    {0xFFFFFFFFFFFFE0C5, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, 
    {0xFFFFFFFFFFFFFFC7, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF}, 
    {0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF} 
};

更新：我想，也许数字是比特，所以如果我转换3张十六进制数到位，然后将它们组合成一个BigInteger我得到一个正确的号码。但结果是错误的。我在SageMath（类似于python）中编写了以下代码，并且获得了以下图表。

arr = [ 
    [0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x1FFFFFFFFFFFFFFF], 
    [0xE0C81DA0D6A8BD22, 0x161ABD186DA13542, 0x5CEF2C248806C827], 
    [0x8D026C4E14BC7408, 0x4344C125B3533F22, 0x9186506BCC065F20], 
    [0x10AC7CEC7D7E2A3B, 0x5D62CE65E6217813, 0xBAAB5F82BCDB43B3], 
    [0x709C92996E94D801, 0x1411F551608E4D22, 0xD7D9769FAD23BCB1], 
    [0x6287D827008404B7, 0x7E1526D618902F20, 0xEA9BE2F4D6DDB5ED], 
    [0x34CBDC118C15F40E, 0xE7D2A13787E94674, 0xF58A99474919B8C9], 
    [0xD521F7EBBBE8C3A2, 0xE8A773D9A1EA0AAB, 0xFB5117812753B7B8], 
    [0xC3D9E58131089A6A, 0x148CB49FF716491B, 0xFE151BD0928596D3], 
    [0x2E060C4A842A27F6, 0x07E44D009ADB0049, 0xFF487508BA9F7208], 
    [0xFCEDEFCFAA887582, 0x1A5409BF5D4B039E, 0xFFC16686270CFC82], 
    [0x4FE22E5DF9FAAC20, 0xFDC99BFE0F991958, 0xFFEC8AC3C159431B], 
    [0xA36605F81B14FEDF, 0xA6FCD4C13F4AFCE0, 0xFFFA7DF4B6E92C28], 
    [0x9D1FDCFF97BBC957, 0x4B869C6286ED0BB5, 0xFFFE94BB4554B5AC], 
    [0x6B3EEBA74AAD104B, 0xEC72329E974D63C7, 0xFFFFAADE1B1CAA95], 
    [0x48C8DA4009C10760, 0x337F6316C1FF0A59, 0xFFFFEDDC1C6436DC], 
    [0x84480A71312F35E7, 0xD95E7B2CD6933C97, 0xFFFFFC7C9DC2569A], 
    [0x23C01DAC1513FA0F, 0x8E0B132AE72F729F, 0xFFFFFF61BC337FED], 
    [0x90C89D6570165907, 0x05B9D725AAEA5CAD, 0xFFFFFFE6B3CF05F7], 
    [0x692E2A94C500EC7D, 0x99E8F72C370F27A6, 0xFFFFFFFC53EA610E], 
    [0x28C2998CEAE37CC8, 0xC6E2F0D7CAFA9AB8, 0xFFFFFFFF841943DE], 
    [0xC515CF4CB0130256, 0x4745913CB4F9E4DD, 0xFFFFFFFFF12D07EC], 
    [0x39F0ECEA047D6E3A, 0xEE62D42142AC6544, 0xFFFFFFFFFE63E348], 
    [0xDF11BB25B50462D6, 0x064A0C6CC136E943, 0xFFFFFFFFFFD762C7], 
    [0xCDBA0DD69FD2EA0F, 0xC672F3A74DB0F175, 0xFFFFFFFFFFFC5E37], 
    [0xFDB966A75F3604D9, 0x6ABEF8B144723D83, 0xFFFFFFFFFFFFB48F], 
    [0x3C4FECBB600740D1, 0x697598CEADD71A15, 0xFFFFFFFFFFFFFA72], 
    [0x1574CC916D60E673, 0x12F5A30DD99D7051, 0xFFFFFFFFFFFFFFA1], 
    [0xDD3DCD1B9CB7321D, 0x4016ED3E05883572, 0xFFFFFFFFFFFFFFFA], 
    [0xB4A4E8CF3DF79A7A, 0xAF22D9AFAD5A73CF, 0xFFFFFFFFFFFFFFFF], 
    [0x91056A8196F74466, 0xFBF88681905332BA, 0xFFFFFFFFFFFFFFFF], 
    [0x965B9ED9BD366C04, 0xFFD16385AF29A51F, 0xFFFFFFFFFFFFFFFF], 
    [0xF05F75D38F2D28A3, 0xFFFE16FF8EA2B60C, 0xFFFFFFFFFFFFFFFF], 
    [0x77E35C8980421EE8, 0xFFFFEDD3C9DDC7E8, 0xFFFFFFFFFFFFFFFF], 
    [0x92783617956F140A, 0xFFFFFF63392B6E8F, 0xFFFFFFFFFFFFFFFF], 
    [0xA536DC994639AD78, 0xFFFFFFFB3592B3D1, 0xFFFFFFFFFFFFFFFF], 
    [0x8F3A871874DD9FD5, 0xFFFFFFFFDE04A5BB, 0xFFFFFFFFFFFFFFFF], 
    [0x310DE3650170B717, 0xFFFFFFFFFF257152, 0xFFFFFFFFFFFFFFFF], 
    [0x1F21A853A422F8CC, 0xFFFFFFFFFFFB057B, 0xFFFFFFFFFFFFFFFF], 
    [0x3CA9D5C6DB4EE2BA, 0xFFFFFFFFFFFFE5AD, 0xFFFFFFFFFFFFFFFF], 
    [0xCFD9CE958E59869C, 0xFFFFFFFFFFFFFF81, 0xFFFFFFFFFFFFFFFF], 
    [0xDB8E1F91D955C452, 0xFFFFFFFFFFFFFFFD, 0xFFFFFFFFFFFFFFFF], 
    [0xF78EE3A8E99E08C3, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF], 
    [0xFFE1D7858BABDA25, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF], 
    [0xFFFF9E52E32CAB4A, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF], 
    [0xFFFFFEE13217574F, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF], 
    [0xFFFFFFFD04888041, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF], 
    [0xFFFFFFFFF8CD8A56, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF], 
    [0xFFFFFFFFFFF04111, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF], 
    [0xFFFFFFFFFFFFE0C5, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF], 
    [0xFFFFFFFFFFFFFFC7, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF], 
    [0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF] 
] 

arr2 = [] 

for element in arr: 
    todo = "" 
    for val in element: 
     todo = todo + str(bin(val))[2:] 

    arr2.append(int(str(todo), base=2)) 

bar_chart(arr2)

我的做法是无效的，因为条形图中值不增加的方式（如C代码实际作者说，这是）我没注意小尾数概念。

问题：如何正确转换这些3十六进制每个结构成的BigInteger（JAVA）或Python的多头或只得到位的正确值。

更新：我取代第三和第一，仍然条形图不按递增的方式。 Test it here.

来源

2016-12-22 Node.JS

首先，这个问题是不是C *和*的Java *和* Python的，哈哈。其次，这当然是重复的。这里有一个这样的问题，回答正是为这种情况做：http://stackoverflow.com/a/2182184/2402061 –

请不要标记[标签：蟒蛇]和[标签：java的]只是因为你_mentions_ Python的问题和Java。 – ForceBru

在Java中，你可以使用'Long.reverseBytes（长）'。 – Bubletan

我会在Java中承担类似的结构：

long rlwe_table[][] = { 
    {0xFFFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL, 0x1FFFFFFFFFFFFFFFL}, 
    {0xE0C81DA0D6A8BD22L, 0x161ABD186DA13542L, 0x5CEF2C248806C827L}, 
    {0x8D026C4E14BC7408L, 0x4344C125B3533F22L, 0x9186506BCC065F20L}, 
    {0x10AC7CEC7D7E2A3BL, 0x5D62CE65E6217813L, 0xBAAB5F82BCDB43B3L}, 
    {0x709C92996E94D801L, 0x1411F551608E4D22L, 0xD7D9769FAD23BCB1L}, 
    {0x6287D827008404B7L, 0x7E1526D618902F20L, 0xEA9BE2F4D6DDB5EDL}, 
    {0x34CBDC118C15F40EL, 0xE7D2A13787E94674L, 0xF58A99474919B8C9L}, 
    {0xD521F7EBBBE8C3A2L, 0xE8A773D9A1EA0AABL, 0xFB5117812753B7B8L}, 
    {0xC3D9E58131089A6AL, 0x148CB49FF716491BL, 0xFE151BD0928596D3L}, 
    {0x2E060C4A842A27F6L, 0x07E44D009ADB0049L, 0xFF487508BA9F7208L}, 
    {0xFCEDEFCFAA887582L, 0x1A5409BF5D4B039EL, 0xFFC16686270CFC82L}, 
    {0x4FE22E5DF9FAAC20L, 0xFDC99BFE0F991958L, 0xFFEC8AC3C159431BL}, 
    {0xA36605F81B14FEDFL, 0xA6FCD4C13F4AFCE0L, 0xFFFA7DF4B6E92C28L}, 
    {0x9D1FDCFF97BBC957L, 0x4B869C6286ED0BB5L, 0xFFFE94BB4554B5ACL}, 
    {0x6B3EEBA74AAD104BL, 0xEC72329E974D63C7L, 0xFFFFAADE1B1CAA95L}, 
    {0x48C8DA4009C10760L, 0x337F6316C1FF0A59L, 0xFFFFEDDC1C6436DCL}, 
    {0x84480A71312F35E7L, 0xD95E7B2CD6933C97L, 0xFFFFFC7C9DC2569AL}, 
    {0x23C01DAC1513FA0FL, 0x8E0B132AE72F729FL, 0xFFFFFF61BC337FEDL}, 
    {0x90C89D6570165907L, 0x05B9D725AAEA5CADL, 0xFFFFFFE6B3CF05F7L}, 
    {0x692E2A94C500EC7DL, 0x99E8F72C370F27A6L, 0xFFFFFFFC53EA610EL}, 
    {0x28C2998CEAE37CC8L, 0xC6E2F0D7CAFA9AB8L, 0xFFFFFFFF841943DEL}, 
    {0xC515CF4CB0130256L, 0x4745913CB4F9E4DDL, 0xFFFFFFFFF12D07ECL}, 
    {0x39F0ECEA047D6E3AL, 0xEE62D42142AC6544L, 0xFFFFFFFFFE63E348L}, 
    {0xDF11BB25B50462D6L, 0x064A0C6CC136E943L, 0xFFFFFFFFFFD762C7L}, 
    {0xCDBA0DD69FD2EA0FL, 0xC672F3A74DB0F175L, 0xFFFFFFFFFFFC5E37L}, 
    {0xFDB966A75F3604D9L, 0x6ABEF8B144723D83L, 0xFFFFFFFFFFFFB48FL}, 
    {0x3C4FECBB600740D1L, 0x697598CEADD71A15L, 0xFFFFFFFFFFFFFA72L}, 
    {0x1574CC916D60E673L, 0x12F5A30DD99D7051L, 0xFFFFFFFFFFFFFFA1L}, 
    {0xDD3DCD1B9CB7321DL, 0x4016ED3E05883572L, 0xFFFFFFFFFFFFFFFAL}, 
    {0xB4A4E8CF3DF79A7AL, 0xAF22D9AFAD5A73CFL, 0xFFFFFFFFFFFFFFFFL}, 
    {0x91056A8196F74466L, 0xFBF88681905332BAL, 0xFFFFFFFFFFFFFFFFL}, 
    {0x965B9ED9BD366C04L, 0xFFD16385AF29A51FL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xF05F75D38F2D28A3L, 0xFFFE16FF8EA2B60CL, 0xFFFFFFFFFFFFFFFFL}, 
    {0x77E35C8980421EE8L, 0xFFFFEDD3C9DDC7E8L, 0xFFFFFFFFFFFFFFFFL}, 
    {0x92783617956F140AL, 0xFFFFFF63392B6E8FL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xA536DC994639AD78L, 0xFFFFFFFB3592B3D1L, 0xFFFFFFFFFFFFFFFFL}, 
    {0x8F3A871874DD9FD5L, 0xFFFFFFFFDE04A5BBL, 0xFFFFFFFFFFFFFFFFL}, 
    {0x310DE3650170B717L, 0xFFFFFFFFFF257152L, 0xFFFFFFFFFFFFFFFFL}, 
    {0x1F21A853A422F8CCL, 0xFFFFFFFFFFFB057BL, 0xFFFFFFFFFFFFFFFFL}, 
    {0x3CA9D5C6DB4EE2BAL, 0xFFFFFFFFFFFFE5ADL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xCFD9CE958E59869CL, 0xFFFFFFFFFFFFFF81L, 0xFFFFFFFFFFFFFFFFL}, 
    {0xDB8E1F91D955C452L, 0xFFFFFFFFFFFFFFFDL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xF78EE3A8E99E08C3L, 0xFFFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xFFE1D7858BABDA25L, 0xFFFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xFFFF9E52E32CAB4AL, 0xFFFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xFFFFFEE13217574FL, 0xFFFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xFFFFFFFD04888041L, 0xFFFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xFFFFFFFFF8CD8A56L, 0xFFFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xFFFFFFFFFFF04111L, 0xFFFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xFFFFFFFFFFFFE0C5L, 0xFFFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xFFFFFFFFFFFFFFC7L, 0xFFFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL}, 
    {0xFFFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL} 
};

如果您希望将它们组合到BigInteger秒的阵列，可以追加数字与shiftLeft和or方法。像这样：

BigInteger[] bigIntegers = new BigInteger[rlwe_table.length]; 

for(int i=0; i<rlwe_table.length; i++){ 
    BigInteger big = BigInteger.valueOf(0); 
    for(int j=0; j<rlwe_table[i].length; j++){ 
     big = big.or(new BigInteger(Long.toHexString(rlwe_table[i][j]),16).shiftLeft(j*64)); 
    } 
    bigIntegers[i] = big; 
}

结果是可变bigIntegers。

来源

2016-12-26 11:30:38 Rei

小尾数为整数（或BigInteger的）

回答

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