Pour commencer ce challenge, on peut essayer de voir si RsaCtfTool ne permet pas de le résoudre simplement. Malheureusement, non.
Il faut se creuser les méninges, et voir que le nombre sept apparaît plusieurs fois dans l'énoncé. Nous allons alors regarder notre module... en base 7.
N=10274622173320909389031395002382723520310683266624262003758324433654540040809219233599998390391541291081480955769558063877739745263628876566148594399190487217520529947703418385797126076202883896285563297412493796455549735516349258737267111485734958124647676862139978578822328063131028977645973314255958832814431129401741363681924246624731580306332996274947224225276913011825249480579351788647303424376829926794897238480915821396590836505557261932201793218787876369479689474390699568395442160695951675495911526788768792712587827140759752600815834201530200102574327547287838813124748635529299343877238787638666002517369183147324348276580386835912162978347500880951405211071469315569907393288673767750500338439908319636060342999154216171420367334387728243762904978917643239586128408102087398429687219613116999755320251996795637299545734755393100528238070409625880097215206538255250563512463977488434914174814989014820102387306536769608806232340706951978003787459755560489338182409731880347246492232556511479625859446872995332197943657987872417697758505073815646447821621770469326686335161275436219144215858159910848423968589115317782429522873529296494028537507162631866445206682695650087594304263021619605307406513658218147729 en base 10
et N=1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000030000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000030000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000010000000000000001000000000000000000000000000000000000000000000000012000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000300000010000000000000000000000000000000000000000000000000000000000331000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000010000110000000000000000000000000000000000000000000010000000000000011000000000000000000000000000000000000000000000000011 en base 7
On voit beaucoup de zéros. Mathématiquement, nous pouvons transformer ce nombre en polynôme: N(x) = 1+1x^1+1x^51+1x^52+1x^67+1x^112+1x^113+1x^118+1x^179+1x^423+1x^474+3x^475+3x^476+1x^535+3x^542+2x^723+1x^724+1x^774+1x^790+1x^835+3x^898+1x^1146+3x^1198+1x^1446 Mais nous avons N(x)=p(x)q(x) avec en particulier N(7)=p(7)q(7) où nous retrouvons les p et q générateurs de N. Il suffit de retravailler ce script fait par Alternatif qui est fait pour un problème similaire, mais en base 3 pour pouvoir retrouver le p et le q, qui permettent de trouver le message caché:
DS Bandit pwned - Follow protocol EVE - Brute Ninja
Le flag est donc:
HACKDAY{EVE}