目录
RSA attack
from gmpy2 import *
from Crypto.Util.number import *
import sympy
import random
from secret import flag
p1 = getPrime(1024)
print(p1)
#p1=172071201093945294154292240631809733545154559633386758234063824053438835958515543354911249971174172649606257936857627547311760174511316984409767738981247877005802155796623587461774104951797122995266217334158736848307655543970322950339988489801672160058805422153816950022590644650247595501280192205506649936031
p2 = p1 - random(999,99999)
print(p2)
#p2=172071201093945294154292240631809733545154559633386758234063824053438835958515543354911249971174172649606257936857627547311760174511316984409767738981247877005802155796623587461774104951797122995266217334158736848307655543970322950339988489801672160058805422153816950022590644650247595501280192205506649902034
p_1=1
for i in range(1,p1+1):
p_1*=i
p3 = sympy.nextPrime(p_1 % p2 )
p4 = p3 >> 50 << 50
p = p4
while(isPrime(P)!=1):
P = p + random.randint(0,2**50)
Q = getPrime(1024)
e = 1+1+1
N = P * Q
print(N)
#N=28592245028568852124815768977111125874262599260058745599820769758676575163359612268623240652811172009403854869932602124987089815595007954065785558682294503755479266935877152343298248656222514238984548734114192436817346633473367019138600818158715715935132231386478333980631609437639665255977026081124468935510279104246449817606049991764744352123119281766258347177186790624246492739368005511017524914036614317783472537220720739454744527197507751921840839876863945184171493740832516867733853656800209669179467244407710022070593053034488226101034106881990117738617496520445046561073310892360430531295027470929927226907793
flag=bytes_to_long(flag)
c = pow(flag,e,N)
print(c)
#c=15839981826831548396886036749682663273035548220969819480071392201237477433920362840542848967952612687163860026284987497137578272157113399130705412843449686711908583139117413
尝试了一下小明文攻击，直接开了三次方
import gmpy2
import binascii
c=15839981826831548396886036749682663273035548220969819480071392201237477433920362840542848967952612687163860026284987497137578272157113399130705412843449686711908583139117413
m = gmpy2.iroot(c,3)[0]
print(binascii.unhexlify(hex(m)[2:]))ezCRT
from Crypto.Util.number import *
import gmpy2
from random import shuffle
flag = b"flag is here"
def shuffle_flag(s):
str_list = list(s)
shuffle(str_list)
return ''.join(str_list)
nl = []
el = []
count = 0
while count != 5:
p = getPrime(512)
q = getPrime(512)
n = p * q
phi = (p - 1) * (q - 1)
d = gmpy2.next_prime(bytes_to_long(flag))
e = gmpy2.invert(d, phi)
nl.append(n)
el.append(int(e))
count += 1
print(nl)
print(el)
cl = []
flag = shuffle_flag(flag.decode()).encode()
for i in range(len(nl)):
cl.append(pow(bytes_to_long(flag), el[i], nl[i]))
print(cl)
#n1 = [92568419674731290088321621356482160506897805615722568594108449347104924357404183476911642777855820991398881156764068184840768873749718093598712551142529474514837161712525386555067489900887826033760157015587905876891826276883359425048106383489316555600680137377034136599761900203863336332834524981581608546277, 156396473818563541024482014372866929605198443382524196879362284224099117401220679011156723462510565131555949471059964179767945960498473012008220045105490122503438703770112687917922899337041421537937431868908340506324082719417747902320117904166584374628828367801012533926776313544525573302674702867896838756349, 158394833243620345170313957479796081390446308753163267294427471181012679879060921676287361174926310080500003540773261012005682050743188110335872216992843352902160171999286576526304619756655278142788064189969927027027650043645613441449926633380809295720977302961310978360575684689811662689798196832145977450067, 160088237013152996062303719345275590040820298863729670660621544625451638541931139026114480452748397901155923890465415946150076272684251867169893163248736673419035618274961179288085209456220719404244194802327491684233804878013160262798831738441790443743813368173495029170393018727204042599457829167334217403039, 176125361422384852665447804150030174008849487020728296169340093618559367127086381778331613043595010796295772394708222184703701230685609172767761426620379001062695169120599393984950488304290958534830276649464003949555105491117656796777657620812669612752464591728873199832200616338112460100967288829163217253937]
#e1 = [69312028009355287369151190914681978515224902099126626288106202481561083869512381976466800912049172557479956400189281179789850182367192324370292880508005951892909864237831856642160554901550928757105750738313195248541515727624216048436593804176317465366380022764459799506858495981817822670957526705611211712923, 75652848678989239962391202584125835503829570694373189157636155436633908234362973839251550542975725789188895010096917574118924190081886365041870173203566890015476761857546914959928731140619341634983144909962106759048918025248827973161384045263311189477657141886093632791593341193393085433749877270828641736687, 33787880341418355427411601538315129862488529656310145182009801227014512555036822623215545927750632031483856865027938518144081751233475248361490189179988637342429805607352670543555743822390555949569061340741015073482051059972283793490798701339277926430357560613555427570475360496737455291914090967005368044847, 45894271603047945281790624112313938740541711331584775481261776728213544262108835859642003140814571796838418889270625806159755478669858113687476417240730385707171289922064965084283027730393146219788228689778873266618663473231744646293406030907691363263939114550226424730102211751706087680590823466426973879111, 39462780066564051085365889083337472288277223628014907704844994419242541623368920096395581667207909872944692627394665038729398405841875334128211337544205143876652949004817962123951132753801707134333132359039376283331685997619531570270269964807335633423631078057345827010794671894948828680193958561375351954627]
#c1 = [706565317398633346290694952311166623770389747503953970254889622211015097472765489676349936599997109100148837713409666075736711752497174928509516666210124850782396573268200919345005742905131769799719677758163730270857245509037860252700476102090438501579886321486095767737006847692632649652528793934802014895, 39976293505792731417500342473259466413746324373570160856607039564687056797068114044891309890160001547746290678089875953230720229396293686037539133378586045964793387433679304899158546834837314101138069400994334720071006048815998660691472991971598192116289517127819703723844842002711298154106615035755646791235, 82622936948791971063481195310587447614375265630407688161651173440160941964839173273115526802240672776681580169092371677673709037579318090622040018030730165371997331146171751228791524747622285256591779419274845659567001522182995468819720594650389854677582186770321424062935881407083956991646633760500152137305, 47924672523033740219454774309397006543851002473271747603676349322670782245519637286314088457132590816165876451615235937683074852920250584155682791595116359054889940842281324709426616771765312825842634237678243213350551342690870568516232078792788925700389762945955053433276153136302757700081859531596237286407, 157462720644970256050843434459828247139256140406409429896418317109064365936294939244159292550184482469972819258184119865598346921909220060266145241164734603316978286567811044606538176157224828857158099074286931716459626013079677895357212211176535500327064375073662684801175545519382470886239209020257096407424]
类似于rsa-crt攻击，但e是变化的，分析代码发现，每次的加密所用的d都为一样的，考虑为common private key attack
构造相应的格子，得到dM
import binascii
n1 = [92568419674731290088321621356482160506897805615722568594108449347104924357404183476911642777855820991398881156764068184840768873749718093598712551142529474514837161712525386555067489900887826033760157015587905876891826276883359425048106383489316555600680137377034136599761900203863336332834524981581608546277, 156396473818563541024482014372866929605198443382524196879362284224099117401220679011156723462510565131555949471059964179767945960498473012008220045105490122503438703770112687917922899337041421537937431868908340506324082719417747902320117904166584374628828367801012533926776313544525573302674702867896838756349, 158394833243620345170313957479796081390446308753163267294427471181012679879060921676287361174926310080500003540773261012005682050743188110335872216992843352902160171999286576526304619756655278142788064189969927027027650043645613441449926633380809295720977302961310978360575684689811662689798196832145977450067, 160088237013152996062303719345275590040820298863729670660621544625451638541931139026114480452748397901155923890465415946150076272684251867169893163248736673419035618274961179288085209456220719404244194802327491684233804878013160262798831738441790443743813368173495029170393018727204042599457829167334217403039, 176125361422384852665447804150030174008849487020728296169340093618559367127086381778331613043595010796295772394708222184703701230685609172767761426620379001062695169120599393984950488304290958534830276649464003949555105491117656796777657620812669612752464591728873199832200616338112460100967288829163217253937]
e1 = [69312028009355287369151190914681978515224902099126626288106202481561083869512381976466800912049172557479956400189281179789850182367192324370292880508005951892909864237831856642160554901550928757105750738313195248541515727624216048436593804176317465366380022764459799506858495981817822670957526705611211712923, 75652848678989239962391202584125835503829570694373189157636155436633908234362973839251550542975725789188895010096917574118924190081886365041870173203566890015476761857546914959928731140619341634983144909962106759048918025248827973161384045263311189477657141886093632791593341193393085433749877270828641736687, 33787880341418355427411601538315129862488529656310145182009801227014512555036822623215545927750632031483856865027938518144081751233475248361490189179988637342429805607352670543555743822390555949569061340741015073482051059972283793490798701339277926430357560613555427570475360496737455291914090967005368044847, 45894271603047945281790624112313938740541711331584775481261776728213544262108835859642003140814571796838418889270625806159755478669858113687476417240730385707171289922064965084283027730393146219788228689778873266618663473231744646293406030907691363263939114550226424730102211751706087680590823466426973879111, 39462780066564051085365889083337472288277223628014907704844994419242541623368920096395581667207909872944692627394665038729398405841875334128211337544205143876652949004817962123951132753801707134333132359039376283331685997619531570270269964807335633423631078057345827010794671894948828680193958561375351954627]
c1 = [706565317398633346290694952311166623770389747503953970254889622211015097472765489676349936599997109100148837713409666075736711752497174928509516666210124850782396573268200919345005742905131769799719677758163730270857245509037860252700476102090438501579886321486095767737006847692632649652528793934802014895, 39976293505792731417500342473259466413746324373570160856607039564687056797068114044891309890160001547746290678089875953230720229396293686037539133378586045964793387433679304899158546834837314101138069400994334720071006048815998660691472991971598192116289517127819703723844842002711298154106615035755646791235, 82622936948791971063481195310587447614375265630407688161651173440160941964839173273115526802240672776681580169092371677673709037579318090622040018030730165371997331146171751228791524747622285256591779419274845659567001522182995468819720594650389854677582186770321424062935881407083956991646633760500152137305, 47924672523033740219454774309397006543851002473271747603676349322670782245519637286314088457132590816165876451615235937683074852920250584155682791595116359054889940842281324709426616771765312825842634237678243213350551342690870568516232078792788925700389762945955053433276153136302757700081859531596237286407, 157462720644970256050843434459828247139256140406409429896418317109064365936294939244159292550184482469972819258184119865598346921909220060266145241164734603316978286567811044606538176157224828857158099074286931716459626013079677895357212211176535500327064375073662684801175545519382470886239209020257096407424]
#M = gmpy2.iroot(n1[4],2)
M = 13271223056764016754269527611397929859013802199370388499804617460328353577862412658459629494948675785123714159315253262225202241852440732158697976396558555
mat = [[M,e1[0],e1[1],e1[2],e1[3],e1[4]],
[0,-n1[0],0,0,0,0],
[0,0,-n1[1],0,0,0],
[0,0,0,-n1[2],0,0],
[0,0,0,0,-n1[3],0],
[0,0,0,0,0,-n1[4]]]
mt = matrix(ZZ,mat)
dM = mt.LLL()[0][0]
print(dM)
d = dM //M
print(binascii.unhexlify(hex(d)[2:]))cubic
#!/usr/bin/env python3
from math import gcd
from functools import reduce
from fractions import Fraction as Frac
N = 6
def read_num(prompt):
try:
num = int(input(prompt))
except:
return 0
return num if num > 0 else 0
print(f"Please give me {N} pairs of positive integers (x,y,z) "
f"satisfying the equation `x/(y+z) + y/(z+x) + z/(x+y) = {N}`\n")
anss = []
mark = 0
for i in range(N):
x = read_num("[>] x: ")
y = read_num("[>] y: ")
z = read_num("[>] z: ")
if x * y * z == 0: # positive integer
mark = 1
print("This is not what i want!\n")
break
if reduce(gcd, [x, y, z]) != 1: # (kx, ky, kz)
mark = 1
print("This is not what i want!\n")
break
if Frac(x, y+z) + Frac(y, z+x) + Frac(z, x+y) != N:
mark = 1
print("This is not what i want!\n")
break
ans = tuple(sorted([x, y, z])) # (y, x, z)
if ans in anss:
mark = 1
print("This is not what i want!\n")
break
else:
print("You are right!\n")
anss.append(ans)
if mark == 0:
flag = open('/flag', 'r').read()
print("flag is: " + flag + "\n")
else:
print("Something wrong!\n")
丢番图问题，椭圆曲线下的数学问题
首先求解基底
from fractions import Fraction as Frac
from math import gcd
for x in range(-100,100):
for y in range(-100,100):
for z in range(-100,100):
if gcd(x, gcd(y, z)) == 1:
if x**3 + y**3 + z**3 - 5 * x**2 * (y + z) - 5 * y**2 * (z + x) - 5 * z**2 * (x + y) - 9 * x * y * z == 0:
print((x, y, z))得到两组可用基底(-23, -7, 3) (-8, -7, 5)
使用http://magma.maths.usyd.edu.au/calc/和脚本
R<x,y,z> := RationalFunctionField(Rationals(),3);
problem := ((x/(y+z) + y/(x+z) + z/(x+y)) - 6) ;
Evaluate(problem,[-23, -7, 3]);
problem*Denominator(problem);
P2<x,y,z> := 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![-23, -7, 3];
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]);
if ((X gt 0) and (Y gt 0)) then
printf "Z=%o\n",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;由于网站篇幅限制，数字过大，不能显示完全，可能会导致数据丢失，尝试X Y Z分别输出，然后写个交互脚本进行字符发送
密码👵👵