【公開鍵{e, n}】RSA暗号で会話するスレ【秘密鍵d】
1 ：１３２人目の素数さん：
Mathematicaでのアルゴリズム記述
（Mathematicaが無くてもアルゴリズムとUnicodeから一応計算可能ですよ^^;）
(* 定義 *)
encrypt[m_, e_, n_] = Mod[m^e, n];
decrypt[c_, d_, n_] = Mod[c^d, n];
p = Prime[60];
q = Prime[70];
n = p q;
phin = (p - 1) (q - 1);
e = 2;
While[GCD[e, phin] != 1, e++];
{g, {d, k}} = ExtendedGCD[e, phin];
d = If[d < 0, d + phin, d];
(* テスト1 *)
m1 = 1234;
c1 = encrypt[m1, e, n]
decrypt[c1, d, n]
(* テスト2 *)
m2 = ToCharacterCode["Nurupo"]
c2 = encrypt[m2, e, n]
FromCharacterCode[decrypt[c2, d, n]]
じゃーまず俺からね〜！
公開鍵：{e, n} = {11, 98069}
暗号文：c = {40664, 56301, 18167, 63083, 242, 82112, 39909, 47708, 61841, 5624, \
64264, 76144, 89552, 2690, 53670, 75353}
（Mathematicaが無くてもアルゴリズムとUnicodeから一応計算可能ですよ^^;）
(* 定義 *)
encrypt[m_, e_, n_] = Mod[m^e, n];
decrypt[c_, d_, n_] = Mod[c^d, n];
p = Prime[60];
q = Prime[70];
n = p q;
phin = (p - 1) (q - 1);
e = 2;
While[GCD[e, phin] != 1, e++];
{g, {d, k}} = ExtendedGCD[e, phin];
d = If[d < 0, d + phin, d];
(* テスト1 *)
m1 = 1234;
c1 = encrypt[m1, e, n]
decrypt[c1, d, n]
(* テスト2 *)
m2 = ToCharacterCode["Nurupo"]
c2 = encrypt[m2, e, n]
FromCharacterCode[decrypt[c2, d, n]]
じゃーまず俺からね〜！
公開鍵：{e, n} = {11, 98069}
暗号文：c = {40664, 56301, 18167, 63083, 242, 82112, 39909, 47708, 61841, 5624, \
64264, 76144, 89552, 2690, 53670, 75353}
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2 ：１３２人目の素数さん：2008/10/27(月) 02:25:20
小さい数だから秘密鍵をクラックしろってこと？
暇だからrubyで解読してみる
暇だからrubyで解読してみる
3 ：１３２人目の素数さん：2008/10/27(月) 02:38:15
d=44291
>>3
今計算できたとこなんだから先に書かないでよ＾＾；
今計算できたとこなんだから先に書かないでよ＾＾；
>>5
暗号化されてないですね＾＾；
暗号化されてないですね＾＾；
8 ：１３２人目の素数さん：2008/10/27(月) 03:15:50
で、どうするよこのスレ…
ごめん>>6はUTF-8だから解読できないかも
>>7 ﾂｯｺﾐありがとう
12 ：１３２人目の素数さん：2008/10/27(月) 20:44:39
>>10
にしてはやるなぁ
にしてはやるなぁ
13 ：１３２人目の素数さん：2008/10/27(月) 21:18:05
>>6のやつUTF-8としてやってみたけどうまくいかない
>>10と同じ文字列だとしてUTF-8で暗号化するとこうなった
{81729, 83270, 26268, 90533, 1982, 74874, 81729, 94586, 64781, 70272, 53764, 64612, 70272, 53764, 61692}
>>10と同じ文字列だとしてUTF-8で暗号化するとこうなった
{81729, 83270, 26268, 90533, 1982, 74874, 81729, 94586, 64781, 70272, 53764, 64612, 70272, 53764, 61692}
15 ：１３２人目の素数さん：2008/10/27(月) 23:01:47
Mod[m^e, n]が一対一の写像になることの証明って簡単ですか？
16 ：１３２人目の素数さん：2008/10/28(火) 01:03:58
{61164, 49400, 17301, 64264, 40664, 56301, 18167, 63083, 87271, \
27880, 30955, 1054, 2690, 31553, 96180, 96180, 96180, 21390, 72633, \
28161, 27880, 30955, 40664, 15813, 84069, 41809, 41809, 41809, 21390, \
86430, 74162, 82094, 18647, 74162, 82094, 8322, 48943, 61767, 19742, \
48943, 58298, 8322, 93087, 74162, 48943, 82094, 82094, 8322, 18647, \
82094, 18647, 8322, 74162, 95790, 18647, 93087, 93087, 8322, 19742, \
57554, 95790, 74162, 82094, 8322, 48943, 48943, 57554, 93087, 93087, \
8322, 58298, 18647, 48943, 95790, 74162, 8322, 82094, 57554, 18647, \
19742, 8322, 95790, 57554, 48943, 48943, 95790, 8322, 48943, 95790, \
74162, 48943, 19742, 8322, 93087, 95790, 48943, 93087, 18647, 8322, \
93087, 18647, 74162, 58298, 58298, 8322, 18647, 19742, 48943, 74162, \
48943, 8322, 95790, 93087, 19742, 93087, 57554, 8322, 82094, 95790, \
95790, 74162, 74162, 8322, 48943, 95790, 93087, 58298, 48943, 8322, \
18647, 48943, 61767, 82094, 57554, 8322, 74162, 82094, 48943, 18647, \
74162, 8322, 74162, 19742, 74162, 18647, 58298, 8322, 95790, 74162, \
48943, 19742, 57554, 82196}
27880, 30955, 1054, 2690, 31553, 96180, 96180, 96180, 21390, 72633, \
28161, 27880, 30955, 40664, 15813, 84069, 41809, 41809, 41809, 21390, \
86430, 74162, 82094, 18647, 74162, 82094, 8322, 48943, 61767, 19742, \
48943, 58298, 8322, 93087, 74162, 48943, 82094, 82094, 8322, 18647, \
82094, 18647, 8322, 74162, 95790, 18647, 93087, 93087, 8322, 19742, \
57554, 95790, 74162, 82094, 8322, 48943, 48943, 57554, 93087, 93087, \
8322, 58298, 18647, 48943, 95790, 74162, 8322, 82094, 57554, 18647, \
19742, 8322, 95790, 57554, 48943, 48943, 95790, 8322, 48943, 95790, \
74162, 48943, 19742, 8322, 93087, 95790, 48943, 93087, 18647, 8322, \
93087, 18647, 74162, 58298, 58298, 8322, 18647, 19742, 48943, 74162, \
48943, 8322, 95790, 93087, 19742, 93087, 57554, 8322, 82094, 95790, \
95790, 74162, 74162, 8322, 48943, 95790, 93087, 58298, 48943, 8322, \
18647, 48943, 61767, 82094, 57554, 8322, 74162, 82094, 48943, 18647, \
74162, 8322, 74162, 19742, 74162, 18647, 58298, 8322, 95790, 74162, \
48943, 19742, 57554, 82196}
17 ：１３２人目の素数さん：2008/10/28(火) 02:28:52
{18203,18203,48943,74162,605,9250,28161,6377,2690,66876,12521,69327,63083,57743,82112,\
81886,40300,66876,72633,28161,27880,7868,49966,1914,90245,1054,22641,21390,12521,\
76144,92638,89552,76144,13049,17545,41923,81886,66876,75353,22641,21390,10502,\
97661,10052,97661,48319,63468,39920,57511,27188,38597,57743,89831,66876,48943,\
57554,18647,82094,21201,8746,57511,38597,69523,35735,48319,59199,69523,72633,28161,\
50289,22641,21390,38246,38597,38597,27188,37513,57532,57532,40215,48348,32334,\
38597,48348,63468,66756,87875,27188,57532,29602,57532,57554,61767,57532,44331,\
97661,57511,39920,48348,97661,72964,57532,57554,17651,18647,17651,58298,87875,97661,\
66756,38246,38597,39680,72964,22641,21390}
81886,40300,66876,72633,28161,27880,7868,49966,1914,90245,1054,22641,21390,12521,\
76144,92638,89552,76144,13049,17545,41923,81886,66876,75353,22641,21390,10502,\
97661,10052,97661,48319,63468,39920,57511,27188,38597,57743,89831,66876,48943,\
57554,18647,82094,21201,8746,57511,38597,69523,35735,48319,59199,69523,72633,28161,\
50289,22641,21390,38246,38597,38597,27188,37513,57532,57532,40215,48348,32334,\
38597,48348,63468,66756,87875,27188,57532,29602,57532,57554,61767,57532,44331,\
97661,57511,39920,48348,97661,72964,57532,57554,17651,18647,17651,58298,87875,97661,\
66756,38246,38597,39680,72964,22641,21390}
18 ：17：2008/10/28(火) 02:50:50
{ 60768, 41923, 12521, 9250, 28161, 6377, 35273, 81886, 82112, 81886, 40300, 66876, \
72633, 28161, 27880, 9250, 28161, 89552, 91326, 36902, 30046, 90245, 91071, 53670, \
69079, 68727, 44007, 96312, 7868, 23355, 22334, 89552, 53504, 242, 27880, 35598, \
64126, 96428, 80964, 57743, 35273, 81886, 40300, 13049, 90245, 53670, 41923, \
36902, 80778, 36902, 1054, 16193, 81886, 53670, 78658, 41923, 12521, 32067, 76144, \
90245, 1054, 53670, 90245, 75353 }
72633, 28161, 27880, 9250, 28161, 89552, 91326, 36902, 30046, 90245, 91071, 53670, \
69079, 68727, 44007, 96312, 7868, 23355, 22334, 89552, 53504, 242, 27880, 35598, \
64126, 96428, 80964, 57743, 35273, 81886, 40300, 13049, 90245, 53670, 41923, \
36902, 80778, 36902, 1054, 16193, 81886, 53670, 78658, 41923, 12521, 32067, 76144, \
90245, 1054, 53670, 90245, 75353 }
19 ：１３２人目の素数さん：2008/10/29(水) 01:14:38
{64264, 78658, 48943, 89552, 2690, 16193, 56301, 50151, 69277, 96312, \
4028, 11077, 1054, 91326, 56301, 35273, 95619, 15813, 16193, 21390, \
11077, 54215, 64030, 242, 4716, 4028, 35872, 60429, 1914, 49966, \
80778, 35273, 81886, 80778, 36902, 16193, 21390, 76144, 76144, 89552, \
5624, 71814, 27880, 35735, 48319, 59199, 72633, 28161, 6377, 35273, \
81886, 66876, 17301, 64264, 30046, 59862, 27236, 35735, 48319, 59199, \
89552, 5624, 64126, 96428, 90119, 32196, 54215, 33668, 242, 80778, \
35735, 48319, 59199, 72633, 28161, 6377, 35273, 81886, 66876, 242, \
90245, 16193, 21390, 51389, 12521, 30046, 15964, 15112, 79443, 35273, \
7832, 12113, 74161, 12521, 53670, 78658, 48830, 39882, 57743, 90245, \
41923, 36902, 16193, 21390, 21390, 12521, 1054, 15813, 53670, 53504, \
78658, 53504, 78658, 62372, 5624, 64264, 1043, 32067, 90245, 91071, \
49400, 89831, 96277, 96180, 21390, 36822, 12521, 35273, 36902, 91326, \
41923, 53670, 17301, 89552, 72633, 28161, 242, 64030, 96909, 96428, \
64030, 242, 40210, 65156, 12731, 91928, 17301, 81886, 69327, 16193, \
21390, 40664, 78658, 35273, 92638, 53504, 15813, 49400, 41923, 36902, \
53670, 63083, 59862, 70109, 57743, 60768, 41923, 81886, 80778, 36902, \
242, 89831, 96277, 16193, 21390, 91071, 89552, 30046, 35735, 48319, \
59199, 605, 29026, 4028, 43137, 61164, 9303, 46033, 89552, 52568, \
23734, 35273, 81886, 78658, 63083, 15813, 242, 12521, 71739, 32275, \
53504, 15813, 49400, 90245, 96180, 41461, 30046, 21390, 23355, 7499, \
83349, 242, 31850, 85083, 90639, 78658, 49862, 96277, 81886, 74880, \
81886, 36902, 242, 7868, 76144, 242, 68623, 32329, 96428, 43137, \
96180, 96180, 96180, 96180, 96180}
4028, 11077, 1054, 91326, 56301, 35273, 95619, 15813, 16193, 21390, \
11077, 54215, 64030, 242, 4716, 4028, 35872, 60429, 1914, 49966, \
80778, 35273, 81886, 80778, 36902, 16193, 21390, 76144, 76144, 89552, \
5624, 71814, 27880, 35735, 48319, 59199, 72633, 28161, 6377, 35273, \
81886, 66876, 17301, 64264, 30046, 59862, 27236, 35735, 48319, 59199, \
89552, 5624, 64126, 96428, 90119, 32196, 54215, 33668, 242, 80778, \
35735, 48319, 59199, 72633, 28161, 6377, 35273, 81886, 66876, 242, \
90245, 16193, 21390, 51389, 12521, 30046, 15964, 15112, 79443, 35273, \
7832, 12113, 74161, 12521, 53670, 78658, 48830, 39882, 57743, 90245, \
41923, 36902, 16193, 21390, 21390, 12521, 1054, 15813, 53670, 53504, \
78658, 53504, 78658, 62372, 5624, 64264, 1043, 32067, 90245, 91071, \
49400, 89831, 96277, 96180, 21390, 36822, 12521, 35273, 36902, 91326, \
41923, 53670, 17301, 89552, 72633, 28161, 242, 64030, 96909, 96428, \
64030, 242, 40210, 65156, 12731, 91928, 17301, 81886, 69327, 16193, \
21390, 40664, 78658, 35273, 92638, 53504, 15813, 49400, 41923, 36902, \
53670, 63083, 59862, 70109, 57743, 60768, 41923, 81886, 80778, 36902, \
242, 89831, 96277, 16193, 21390, 91071, 89552, 30046, 35735, 48319, \
59199, 605, 29026, 4028, 43137, 61164, 9303, 46033, 89552, 52568, \
23734, 35273, 81886, 78658, 63083, 15813, 242, 12521, 71739, 32275, \
53504, 15813, 49400, 90245, 96180, 41461, 30046, 21390, 23355, 7499, \
83349, 242, 31850, 85083, 90639, 78658, 49862, 96277, 81886, 74880, \
81886, 36902, 242, 7868, 76144, 242, 68623, 32329, 96428, 43137, \
96180, 96180, 96180, 96180, 96180}
20 ：１３２人目の素数さん：2008/10/29(水) 01:16:43
{64413, 89552, 43296, 1054, 36902, 40210, 65156, 41923, 81886, 242, \
5624, 29026, 32329, 21390, 38246, 38597, 38597, 27188, 37513, 57532, \
57532, 38823, 38823, 38823, 66756, 44331, 66756, 38823, 97661, 57253, \
48348, 40215, 97661, 66756, 87875, 27188, 57532, 38597, 27596, 92716, \
27596, 57511, 32334, 30113, 39680, 57511, 57532, 63468, 72964, 97661, \
57253, 57253, 48348, 57253, 57532, 39680, 97661, 38597, 38246, 57532, \
35735, 48319, 59199, 66756, 27188, 40215, 44331, 21390, 38246, 38597, \
38597, 27188, 37513, 57532, 57532, 38823, 38823, 38823, 66756, 44331, \
66756, 38823, 97661, 57253, 48348, 40215, 97661, 66756, 87875, 27188, \
57532, 38597, 27596, 92716, 27596, 57511, 32334, 30113, 39680, 57511, \
57532, 63468, 72964, 97661, 57253, 57253, 48348, 57253, 57532, 97661, \
57511, 32334, 30113, 57532, 72964, 48348, 63468, 38597, 30113, 39920, \
48348, 57253, 57532, 72964, 57511, 38597, 48348, 39920, 97661, 63468, \
92716, 18647, 57532, 66685, 97661, 38597, 38246, 48348, 39680, 97661, \
38597, 57511, 63468, 97661, 58298, 66756, 27188, 40215, 44331}
5624, 29026, 32329, 21390, 38246, 38597, 38597, 27188, 37513, 57532, \
57532, 38823, 38823, 38823, 66756, 44331, 66756, 38823, 97661, 57253, \
48348, 40215, 97661, 66756, 87875, 27188, 57532, 38597, 27596, 92716, \
27596, 57511, 32334, 30113, 39680, 57511, 57532, 63468, 72964, 97661, \
57253, 57253, 48348, 57253, 57532, 39680, 97661, 38597, 38246, 57532, \
35735, 48319, 59199, 66756, 27188, 40215, 44331, 21390, 38246, 38597, \
38597, 27188, 37513, 57532, 57532, 38823, 38823, 38823, 66756, 44331, \
66756, 38823, 97661, 57253, 48348, 40215, 97661, 66756, 87875, 27188, \
57532, 38597, 27596, 92716, 27596, 57511, 32334, 30113, 39680, 57511, \
57532, 63468, 72964, 97661, 57253, 57253, 48348, 57253, 57532, 97661, \
57511, 32334, 30113, 57532, 72964, 48348, 63468, 38597, 30113, 39920, \
48348, 57253, 57532, 72964, 57511, 38597, 48348, 39920, 97661, 63468, \
92716, 18647, 57532, 66685, 97661, 38597, 38246, 48348, 39680, 97661, \
38597, 57511, 63468, 97661, 58298, 66756, 27188, 40215, 44331}
21 ：１３２人目の素数さん：2008/10/29(水) 07:05:28
sageでやれ
うざい
うざい
22 ：１３２人目の素数さん：2008/11/22(土) 16:04:11
どうすれば読めますか？
23 ：１３２人目の素数さん：2008/11/26(水) 19:14:44
うるさい。
24 ：１３２人目の素数さん：2009/01/10(土) 15:43:59
347
25 ：１３２人目の素数さん：2009/01/29(木) 12:59:21
775
26 ：１３２人目の素数さん：2009/02/12(木) 15:51:54
ｑ
27 ：１３２人目の素数さん：2009/02/12(木) 15:52:16
ｑ
28 ：１３２人目の素数さん：2009/04/25(土) 11:20:16
885
29 ：１３２人目の素数さん：
153