Question

我想知道是否有办法将numbers that are in little endians转换为BigInteger或者在python或java中转换为long。他们是in little endians format。这些数字是C结构格式，它们不只是十六进制，所以很容易混淆。

/* 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的，所以如果我将3个十六进制数转换成比特然后将它们组合成一个BigInteger，我得到一个正确的数字。但事实证明这是错误的。我在SageMath中编写了以下代码（类似于python），我得到了下面的图表。

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)

我的方法无效，因为条形图中的值没有增加（正如C代码的实际作者所说的那样）而且我没有注意小端概念。

问题：如何正确地将每个结构中的这3个十六进制转换为BigInteger（java）或Python的长或只是获得正确的位值。

更新：我更换了第三个和第一个，仍然是条形图没有增加的方式。 Test it here.

Answer 1

我将在Java中假设一个类似的结构：

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}
};

如果要将它们组合到BigInteger的数组中，可以使用shiftLeft和or方法追加数字。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;
}

结果是变量bigIntegers。

小端到整数（或BigInteger）

1 个答案: