{"id":154,"date":"2026-06-09T18:11:10","date_gmt":"2026-06-09T10:11:10","guid":{"rendered":"https:\/\/blog.lmoon.cn\/?p=154"},"modified":"2026-06-18T21:15:57","modified_gmt":"2026-06-18T13:15:57","slug":"%e6%89%a9%e5%b1%95%e6%ac%a7%e5%87%a0%e9%87%8c%e5%be%97-2","status":"publish","type":"post","link":"https:\/\/blog.lmoon.cn\/index.php\/2026\/06\/09\/%e6%89%a9%e5%b1%95%e6%ac%a7%e5%87%a0%e9%87%8c%e5%be%97-2\/","title":{"rendered":"\u6269\u5c55\u6b27\u51e0\u91cc\u5f97"},"content":{"rendered":"\n

\u5728\u8bb2\u89e3\u7684\u9898\u76ee\u4e4b\u524d\u4f60\u9700\u8981\u4e86\u89e3\u4e24\u4e2a\u6982\u5ff5\u4e00\u4e2a\u662f\u88f4\u8700\u5b9a\u7406<\/strong>\uff0c\u4e00\u4e2a\u662f\u6269\u5c55\u6b27\u51e0\u91cc\u5f97,\u548c\u8f97\u8f6c\u76f8\u9664\u6cd5\u601d\u60f3<\/p>\n\n\n\n

\u88f4\u8700\u5b9a\u7406<\/strong><\/h2>\n\n\n\n

\u5982\u679ca,b\u5168\u662f\u4e0d\u4e3a0\u7684\u6574\u6570\uff0c\u5219\u6709\u6574\u6570x,y\u4f7fax+by=gcd(a,b)=gcd(b,a%b)<\/p>\n\n\n\n

\u63a8\u8bba<\/h3>\n\n\n\n

1.\u5982\u679ca,b\u4e92\u8d28\u90a3\u4e48\u53ef\u4ee5\u5f97\u5230\u5f53\u4e14\u4ec5\u5f53\u5b58\u5728\u6574\u6570x,y\uff0c\u4f7f\u5f97ax+by=1<\/p>\n\n\n\n

2.\u5982\u679ca,b\u4e0d\u5168\u4e3a0\uff0c\u5e76\u4e14ax*by=c\u6709\u89e3\uff0c\u90a3\u4e48c\u4e00\u5b9a\u662fgcd(a,b)\u7684\u6574\u6570\u500d<\/p>\n\n\n\n

3.a,b\u4e24\u9879\u53ef\u4ee5\u5e7f\u4e3a\u591a\u9879<\/p>\n\n\n\n

4.\u5982\u679c\u5728\u4fdd\u8bc1a,b,c,\u90fd\u4e0d\u53d8\u7684\u60c5\u51b5\u4e0b\uff0cx,y\u4e5f\u662f\u591a\u89e3\u7684<\/p>\n\n\n\n

\u63a8\u8bba4\u8bc1\u660e<\/h2>\n\n\n\n

\u524d\u63d0\u5f97\u5230\u4e86\u7279\u89e3\u7684x,y\u7684\u524d\u63d0\u4e0b\uff0c\u6c42\u51fa\u901a\u89e3<\/p>\n\n\n\n

\u5e94\u4e3ax,y\u7b26\u5408<\/p>\n\n\n\n

ax+by=gcd(a,b)<\/p>\n\n\n\n

\u4ee4x=x+kb, y=y-ka<\/p>\n\n\n\n

\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u5f97\u5230<\/p>\n\n\n\n

a*(x+kb)+b * (y-ka)<\/p>\n\n\n\n

=a*x+b *y=gcd(a,b)<\/p>\n\n\n\n

\u8bba\u8bc1\u6210\u529f<\/p>\n\n\n\n

\u8f97\u8f6c\u76f8\u9664\u6cd5<\/h2>\n\n\n\n

\u8f97\u8f6c\u76f8\u9664\u6cd5\u7684\u6d41\u7a0b\u5982\u4e0b<\/p>\n\n\n\n

gcd(a,b)\\\\\n1.=gcd(b,a\\%b) \\;\u4ee4a\\%b\u4e3ar1 \\; \u4e0b\u9762\u540c\u7406 \\\\\n2.=gcd(r1,b\\% r1)\\\\\n3.=gcd(r2,r1\\%r2)\\\\\n\u4e00\u76f4\u5230\\\\\n4.gcd(r_n,0)\u65f6\u7ed3\u675f\\\\\n\u6b64\u65f6\u7684r_n\u5c31\u662f\u6700\u5927\u516c\u56e0\u6570<\/pre><\/div>\n\n\n\n
\u5c1d\u8bd5\u7406\u89e3\u4e0b\u9762\u7684\u8fc7\u7a0b<\/h4>\n\n\n\n
\u5f53a=120,b=170\u662f\u6c42\u51fa\u4e00\u7ec4x,y\u4f7fax+by=gcd(a,b)\u6210\u7acb<\/p>\n\n\n\n
gcd(220,170)=10,\u8fc7\u7a0b\u5982\u4e0b\uff1a<\/p>\n\n\n\n
1.gcd(220,170)\\\\\n2 .gcd(170,50)\\\\\n3.gcd(50,20)\\\\\n4.gcd(20,10)\\\\\n5.gcd(10,0)\\\\\n\u6700\u7ec8\u5f97\u5230\u516c\u56e0\u6570\u4e3a10<\/pre><\/div>\n\n\n\n
\u7136\u540e\u63a5\u4e0b\u6765\u5c31\u662f\u6c42\u89e3x,y\uff0c\u6211\u4eec\u77e5\u9053\u77e5\u9053\u4ece\u4e0a\u5f80\u4e0b\u6c42\u662f\u4e0d\u884c\u7684\uff0c\u90a3\u4e48\u5c31\u53cd\u8fc7\u6765\u91cd\u4e0b\u5f80\u4e0a\u6c42\uff0c\u56e0\u4e3a\u4ece\u4e0b\u5f80\u4e0a\u6211\u4eec\u6709\u591a\u4e86\u4e00\u4e2a\u5173\u7cfb\u5c31\u662f\u4e0a\u4e0b\u4e4b\u95f4\u53ef\u4ee5\u76f4\u63a5\u8fdb\u884c\u6570\u5b57\u7684\u66ff\u6362\u3002<\/p>\n\n\n\n
\u4e00\u6b65\u4e00\u6b65\u770b\uff0c\u4e3b\u8981\u662f\u770b\u5f97\u5230\u7684\u4f59\u6570\u90e8\u5206\u7684\u6765\u6e90\\\\\n10=50 \\% 20 =50-2*20\\\\\n10=50-2*(170 \\%50)=50-2*(170-3*50)\n\\\\10=7*50-2*170\\\\\n10=7*(220\\%170)-2*170=7*(220-170)-2*170\\\\\n10=7*220-9*170\n\\\\10=7*220+(-9)*170<\/pre><\/div>\n\n\n\n
\u8fd9\u6837\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u4e00\u7ec4x,y.<\/p>\n\n\n\n
\u6269\u5c55\u6b27\u51e0\u91cc\u5f97\u7b97\u6cd5<\/h2>\n\n\n\n
\u5176\u5b9e\u8fd9\u4e2a\u662f\u4e3a\u4e86\u6269\u5c55\u6b27\u51e0\u91cc\u5f97\u7b97\u6cd5\u5c31\u662f\u4e00\u4e2a\u4ee3\u7801\u6ca1\u6709\u989d\u5916\u7684\u5b9a\u4e49\uff0c\u5176\u76ee\u7684\u5c31\u662f\u4e3a\u4e86\u89e3\u51fa\u4efb\u610f\u7b26\u5408\u88f4\u8700\u5b9a\u7406\u7684ab\uff0c\u90fd\u53ef\u4ee5\u8ba9\u5176\u76f4\u63a5\u8f93\u51fa\u4e00\u7ec4\u7279\u89e3x,y.\u56e0\u6b64\u4ed6\u9700\u8981\u5c06\u4e4b\u524d\u6211\u4eec\u7f16\u5199\u7684\u89e3\u9898\u8fc7\u7a0b\u66f4\u52a0\u7684\u89c4\u8303\u548c\u4ee3\u7801\u5316<\/p>\n\n\n\n
\u6839\u636e\u4e4b\u524d\u7684\u7f16\u5199\u8fc7\u7a0b\u6211\u4eec\u53d1\u73b0\uff0c\u5bf9\u4e8ea,b\u6c42\u51fax,y\u4ed6\u53ef\u4ee5\u5206\u4e3a\u4e24\u90e8\u52061\u90e8\u662f\u4ece\u4e0a\u5f80\u4e0b\u6c42\u51fa\u516c\u56e0\u6570\uff0c\u53e6\u6709\u90e8\u5206\u662f\u5229\u7528\u6c42\u51fa\u516c\u56e0\u6570\u8fdb\u884c\u53cd\u63a8\u51fax,y\u3002<\/p>\n\n\n\n
\u7b2c\u4e00\u90e8\u5206\uff1a<\/p>\n\n\n\n
\u6211\u4eec\u5229\u7528gcd()\u4e00\u76f4\u63a8\uff0c\u53ea\u6709\u5f53\u6700\u540e\u7684b\u7ed3\u679c\u662f0\u65f6\u5019\uff0c\u6211\u4eec\u624d\u4f1a\u5f97\u5230\u516c\u56e0\u6570a<\/p>\n\n\n\n
\u7b2c\u4e8c\u90e8\u5206\uff1a<\/p>\n\n\n\n
\u8fd8\u662f\u4ee5220\uff0c170\u4e3a\u4f8b\u5b50<\/p>\n\n\n\n
\u6211\u4eec\u5f97\u5230\u516c\u56e0\u657010\u7684\u65f6\u5019<\/p>\n\n\n\n
\u5728\u6700\u540e\u4e00\u6b65\u53ef\u4ee5\u5f97\u5230<\/p>\n\n\n\n
\u5bf9\u4e8e\u8fc7\u7a0b5 gcd(10,0)<\/p>\n\n\n\n
10*1+0 * 0=10            \u6b64\u65f6x=1,y=0<\/p>\n\n\n\n
\u8fc7\u7a0b4       gcd(20,10)<\/p>\n\n\n\n
10*1+0 * (20-2*10)=10<\/p>\n\n\n\n
20 * 0 +10 * 1              \u6b64\u65f6x=0,y=1<\/p>\n\n\n\n
\u8fc7\u7a0b3       gcd(50,20)<\/p>\n\n\n\n
20 * 0 +\uff0850-2*20\uff09 * 1=10<\/p>\n\n\n\n
50*1+( – 2) * 20 =10         \u6b64\u65f6  x=1,y=-2<\/p>\n\n\n\n
\u8fc7\u7a0b2       gcd(170,50)<\/p>\n\n\n\n
50 * 1   – 2 * (170-3*50)=10<\/p>\n\n\n\n
(-  2) * 170+50*7  =10     \u6b64\u65f6 x=-2 ,y=7<\/p>\n\n\n\n
\u8fc7\u7a0b1        gcd(220,170)<\/p>\n\n\n\n
-2 * 170 +\uff08220-170\uff09*  7=10<\/p>\n\n\n\n
7*220-9 * 170 =10          \u6b64\u65f6 x=7,y=-9<\/p>\n\n\n\n
\u901a\u8fc7\u8fd9\u4e2a\u8fc7\u7a0b\u6211\u4eec\u4e0d\u96be\u53d1\u73b0\u4e0a\u4e00\u5c42\u7684y1\u53d8\u6210\u4e86\u4e0b\u4e00\u5c42\u7684x2,\u800c\u4e0b\u4e00\u5c42\u7684  y2=a2-a2\/\/b2*b2(\u6b64\u65f6\u7684ab\u90fd\u662f\u5f53\u524d\u5c42\u7684)<\/p>\n\n\n\n
\u5173\u4e8ey2=a2-a2\/\/b2*b2\u539f\u5f0f\u4e3ay=a%b\u4f60\u53ef\u4ee5\u7406\u89e3\u4e3ay\u7b49\u4e8ea\u51cf\u53bba\/\/b\u4e58\u4e8eb\uff0c\u5e94\u4e3a\u5f0f\u6574\u9664\u6240\u4ee5\u5269\u4e0b\u7684\u5c31\u662f\u4f59\u6570\u3002<\/p>\n\n\n\n
\u5373<\/p>\n\n\n\n
x=y<\/p>\n\n\n\n
y=a-a\/\/b*b<\/p>\n\n\n\n
\u6839\u636e\u8fd9\u4e24\u4e2a\u6b65\u9aa4\u8fdb\u884c\u7f16\u5199\u4ee3\u7801\u89e3\u9898\u4ee3\u7801\u5427\uff0c\u6b64\u5916\u89e3\u51fa\u6765\u4e4b\u540e\u53ef\u4ee5\u60f3\u4e00\u4e0b\u5982\u4f55gcd\uff01=1\u65f6\u4f60\u7684\u811a\u672c\u8fd8\u901a\u7528\u5417<\/p>\n\n\n\n
\u9898\u76ee<\/h3>\n\n\n\n
from Crypto.Util.number import *\nflag = b'******'\n\nm1 = bytes_to_long(flag[:len(flag)\/\/2])\nm2 = bytes_to_long(flag[len(flag)\/\/2:])\n\nassert 18608629446895353521310408885845687520013234781800558*m1-14258810472138345414555137649316815272478951117940067*m2 == 1\n<\/code><\/pre>\n\n\n\n
from campus import solve\nfrom Crypto.Util.number import *\na=32966910484103083075640153874030504338744721993701\nb=64656557295323368947703375019596814279122133838868\ndef \u6269\u5c55\u6b27\u51e0\u91cc\u5f97(a,b):\n    if b==0:\n        return 1,0,a\n    else:\n        x,y,g=\u6269\u5c55\u6b27\u51e0\u91cc\u5f97(b,a%b)\n    return y,x-(a\/\/b)*y,g\nsolve=\u6269\u5c55\u6b27\u51e0\u91cc\u5f97(a,b)\nx=abs(solve[0])\ny=abs(solve[1])\nprint(a)\nprint(b)\nwhile(1):\n    x += b\n    y += a\n    flag1=long_to_bytes(x)\n    print(x)\n    flag2=long_to_bytes(y)\n    if b'flag' in long_to_bytes(x):\n        print(flag1+flag2)\n        break<\/code><\/pre>\n\n\n\n
flag{6cd6ac0a-1dd8-4a49-9120-9387b00b5bd5}<\/code><\/pre>\n\n\n\n
\u6590\u6ce2\u90a3\u5951\u6570\u5217-AES<\/h1>\n\n\n\n
from Crypto.Cipher import AES\nfrom Crypto.Util.Padding import pad, unpad\nfrom hashlib import md5\nfrom Crypto.Util.number import*\n\n\nfrom Crypto.Cipher import AES\nfrom Crypto.Util.Padding import unpad\nfrom hashlib import md5\n\niv = bytes.fromhex('a40052319cc54396bd995810e9bff841')\nfinal_cipher = bytes.fromhex(\"d2e8f59adb48d744e28d760afd11c7d8a7954770baca9c773a7078629db659b82b2f92fd7c5dcd684e7a164bf813bd6affe6e726b48a658dd14356c1fe7227d7\")\nkey2=1779979416004714189\nkey2 = key2.to_bytes(16, 'big')\n\nkey1=2427893228399975082453\nkey1 = key1.to_bytes(16, 'big')\ncipher2 = AES.new(key2, AES.MODE_ECB)\n\npadded_ciphertext = cipher2.decrypt(final_cipher)\n\nciphertext = unpad(padded_ciphertext, 16)\n\nprint(ciphertext.hex())\ncipher1 = AES.new(key1, AES.MODE_CBC, iv)\nflag = cipher1.decrypt(ciphertext)\nflag = unpad(flag, 16)\n\nprint(flag)<\/code><\/pre>\n\n\n\n
flag{68d83fb4-48ba-444a-9ae4-c152a26f1b55}<\/code><\/pre>\n\n\n\n
\u6768\u8f89\u4e09\u89d2-RSA<\/h1>\n\n\n\n
from math import gcd\nimport hashlib\n\nphi = 209007847911249849150381994932558950560\n\na = []\n\nfor i in range(65):\n    a.append([1] * (i + 1))\n\n    for j in range(1, i):\n        a[i][j] = a[i - 1][j - 1] + a[i - 1][j]\n\nans = []\n\nfor i in range(65):\n    for j in range(i + 1):\n        e = a[i][j]\n\n        if 1 < e < phi and gcd(e, phi) == 1:\n            ans.append(e)\n\nprint(ans)\nprint(\"\u6570\u91cf:\", len(ans))\nflag  =\"_\".join(map(str, ans))\nprint(flag)\nflag=\"flag{\"+hashlib.md5(flag.encode()).hexdigest()+\"}\"\nprint(flag)<\/code><\/pre>\n\n\n\n
flag{d220e446f2ca6231fc9443646e220dfd}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u5728\u8bb2\u89e3\u7684\u9898\u76ee\u4e4b\u524d\u4f60\u9700\u8981\u4e86\u89e3\u4e24\u4e2a\u6982\u5ff5\u4e00\u4e2a\u662f\u88f4\u8700\u5b9a\u7406\uff0c\u4e00\u4e2a\u662f\u6269\u5c55\u6b27\u51e0\u91cc\u5f97,\u548c\u8f97\u8f6c\u76f8\u9664\u6cd5\u601d\u60f3 \u88f4\u8700\u5b9a\u7406 \u5982\u679ca,b\u5168 […]<\/p>\n","protected":false},"author":1,"featured_media":131,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-154","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-learn"],"_links":{"self":[{"href":"https:\/\/blog.lmoon.cn\/index.php\/wp-json\/wp\/v2\/posts\/154","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.lmoon.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.lmoon.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.lmoon.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.lmoon.cn\/index.php\/wp-json\/wp\/v2\/comments?post=154"}],"version-history":[{"count":1,"href":"https:\/\/blog.lmoon.cn\/index.php\/wp-json\/wp\/v2\/posts\/154\/revisions"}],"predecessor-version":[{"id":155,"href":"https:\/\/blog.lmoon.cn\/index.php\/wp-json\/wp\/v2\/posts\/154\/revisions\/155"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.lmoon.cn\/index.php\/wp-json\/wp\/v2\/media\/131"}],"wp:attachment":[{"href":"https:\/\/blog.lmoon.cn\/index.php\/wp-json\/wp\/v2\/media?parent=154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.lmoon.cn\/index.php\/wp-json\/wp\/v2\/categories?post=154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.lmoon.cn\/index.php\/wp-json\/wp\/v2\/tags?post=154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}