2021数字中国创新大赛虎符网络安全赛道-Eswlnk Blog
智能摘要 AI
该文章描述了一次密码学与逆向工程的比赛经历。比赛中涉及一道密码题和一道逆向工程题，最终排名81名。通过使用Sage数学软件，作者解决了多项式方程，并验证了解的正确性。代码展示了如何定义有理函数域、曲线、椭圆曲线以及迭代点计算的过程。在验证过程中，作者找到了满足条件的解，并确认其正确性。最后部分提到比赛结束后未完成的工作将放在博客中，且正在准备考研。
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x^3 - 5*x^2*y - 5*x^2*z - 5*x*y^2 - 9*x*y*z - 5*x*z^2 + y^3 - 5*y^2*z - 5*y*z^2
    + z^3
X=-23
Y=-7
Z=3
Nee, some coordinate was negative above, I keep in the loop

X=-12605
Y=-26304
Z=24869
Nee, some coordinate was negative above, I keep in the loop

X=-14741015373
Y=-9962121367
Z=7010997913
Nee, some coordinate was negative above, I keep in the loop

X=-344600079128906665
Y=-423865825845143591
Z=399635339857662336
Nee, some coordinate was negative above, I keep in the loop

X=-5601501004856850884990304823
Y=-5289522737323629458801572077
Z=3709408926756435263894180473
Nee, some coordinate was negative above, I keep in the loop

X=-4070627436031293758660082617456391013440
Y=-3778570377038559830581535407335117997939
Z=3947273214056112611641932285192198633259
Nee, some coordinate was negative above, I keep in the loop

X=-1135765668330055092250323976085973407298527010733979623
Y=-1414401999299585078135301950024835142145003502627648887
Z=815923886178656038947477254264840525058302026190395683
Nee, some coordinate was negative above, I keep in the loop

X=-25281620419320048351768026986562305577512151706265133292320809015221455
Y=-16289328882340965120515308879714559149588601003364769362936593893145856
Z=23653053272182405114504253854907737996871323554596696886558694080263471
Nee, some coordinate was negative above, I keep in the loop

X=-1036283675955789870914191341173997441763288957348011417648055320105396267955\
39699048159773
Y=-2144498167749435582495047362564272898767630072564653155222059587647588025645\
15862112581047
Z=64717948697678464838747111173776757364272678503865274880411181224711461102283\
679136152793
Nee, some coordinate was negative above, I keep in the loop

X=-9210733200327079206776755372541629465472159575066558411390159130839118402437\
6586589667869747157372710541019275
Y=-2089699901380100252242640293815183679262147647927586531447673885774778272057\
8088533147052708518040528357255149
Z=89538305283456477498663693926361732820926189248425318358147867876247902898624\
183909917412197607224560490524224
Nee, some coordinate was negative above, I keep in the loop

X=12183432427029058557922642378688032230730902983101212975267528305583238455039\
10071851999217959704024280699759290559009162035102974023
Y=20260869859883222379931520298326390700152988332214525711323500132179943287700\
005601210288797153868533207131302477269470450828233936557
Z=22503240220126838668864264619424948111412000849212232184619673775885644776162\
20767789632257358521952443049813799712386367623925971447
GOT IT!!! x=apple, y=banana, z=pineapple, check the above solution
I evaluated the point to the original problem and yes, it worked!

斜杆不是分数的意思，表示不中断数据的换行。

2021数字中国创新大赛虎符网络安全赛道-Eswlnk Blog 
R := RationalFunctionField(Rationals(),3); 
 
problem := ((x/(y+z) + y/(x+z) + z/(x+y)) - 6) ; 

Evaluate(problem,[-3, 7, 23]); 

problem*Denominator(problem); 

P2 := ProjectiveSpace(Rationals(),2); 
C := Curve(P2,x^3 - 5*x^2*y - 5*x^2*z - 5*x*y^2 - 9*x*y*z - 5*x*z^2 + y^3 - 5*y^2*z - 5*y*z^2 + z^3); 
 
Pt := C![-3, 7, 23]; 
 
E,f := EllipticCurve(C); 
 
g := f^-1; 

for n:= 1 to 100 do 
 
    nPt_inE:=n*f(Pt); 
 
    nPt_inC:=g(nPt_inE); 

    X := Numerator(nPt_inC[1]); 
    Y := Numerator(nPt_inC[2]); 
    Z := Denominator(nPt_inC[1]); 
 
//printf "X=%o\nY=%o\nZ=%o\n",X,Y,Z; 
 
  if ((X gt 0) and (Y gt 0)) then 
       printf "X=%o\nY=%o\nZ=%o\n\n",X,Y,Z; 
       //printf("GOT IT!!! x=apple, y=banana, z=pineapple, check the above solution\n"); 
     //break; 
  else 
     //printf "Nee, some coordinate was negative above, I keep in the loop\n\n"; 
  end if; 
 
end for;    
 
if Evaluate(problem, [X,Y,Z]) eq 0 then 
    printf "I evaluated the point to the original problem and yes, it worked!\n"; 
else 
    printf "Mmm this cannot happen!\n"; 
end if;

reverse 1

2021数字中国创新大赛虎符网络安全赛道-Eswlnk Blog