# picproblem

# 题目

from PIL import Image
from Crypto.Util.number import *
from numpy import array, zeros, uint8
import gmpy2 as gp
import cv2
from key import x,y,kn,hint
image = cv2.imread("flag.jpg")
img_gray = cv2.cvtColor(image,cv2.COLOR_RGB2GRAY)
imagearray = array(img_gray)
h = len(imagearray)
w = len(imagearray[0])
assert 1301149798051259562945444365741194129602596348352064372203373*pow(x, 2) == 1175915431138623881271508290982969935822476052419526528443170552123*pow(y, 2) + 1301149798051259562945444365741194129602596348352064372203373
x1 = round(x/y*0.001, 16)
u1 = y*3650/x
x2 = round(x/y*0.00101, 16)
u2 = y*3675/x
x3 = round(x/y*0.00102, 16)
u3 = y*3680/x
kt = [x1, x2, x3]
temp_image = zeros(shape=[h, w, 3], dtype=uint8)
print(len(temp_image))
print(len(temp_image[0]))
print(len(temp_image[0][1]))
for k in range(0, kn):
    for i in range(0, h):
        for j in range(0, w):
            x1 = u1 * x1 * (1 - x1)
            x2 = u2 * x2 * (1 - x2)
            x3 = u3 * x3 * (1 - x3)
            r1 = int(x1*255)
            r2 = int(x2*255)
            r3 = int(x3*255)
            for t in range(0, 3):
                temp_image[i][j][t] = (((r1+r2) ^ r3)+imagearray[i][j][t]) % 256
    x1 = kt[0]
    x2 = kt[1]
    x3 = kt[2]
encflagarray = Image.fromarray(temp_image)
encflagarray.show()
encflagarray.save("encflag.jpg")
#************************************hint**************************************
m = hint
p = getPrime(512)
q = getPrime(512)
n = p * q
e = 65537
phi = (p-1)*(q-1)
dp = gp.invert(e, p-1)
c = pow(m, e, n)
#n =  85413323752199019806030766630760449394238054889872415531186815348349883843039718091361611175963675771467536496812507338620957273406076058263122453235926619595761737396698699834116678598534261542535530241537247151318756003375573850725841254167462648747492270335084402716816450008370008491069875351593380154253
#dp =  1576424214336939000475035870826282526256046059505538052583882122452307602095912733650442447289122473348318614749578285418144935611098423641334952097553125
#c =  53653254613997095145108444611576166902006080900281661447007750088487109015427510365774527924664116641019490904245926171500894236952984157500461367769566121581870986304353174732328118576440353500038670030097108081972287049673200783198844842527470746431369314585103203118824985764754487936404004696485346196488

先看 hint

dp 泄露

kn=8

然后我们只要知道 x,y 就能求解。比赛的时候完全没意识到这个是佩尔方程(主要还是遇到的不够多)

只化出了这个x2903751y2=1x^2-903751*y^2=1

from gmpy2 import *
def Cal_CF(List):
    List.reverse()
    fenmu = 0
    fenzi = 1
    for i in List:
        fenmu, fenzi = fenzi, i * fenzi + fenmu
    return fenmu, fenzi
t = 903751
m = isqrt(t)
x = t ** (0.5)
a = []
a.append(m)
b = m
c = 1
while a[-1] != 2 * a[0]:
    c = (t - b * b) // c
    tmp = (x + b) / c
    a.append(int(tmp))
    b = a[-1] * c - b
print(len(a) - 1)
print(a)
a = a[:-1]
fenmu, fenzi = Cal_CF(a)
print(fenmu)
print(fenzi)

得到 x,y

求解

from PIL import Image
from Crypto.Util.number import *
from numpy import array, zeros, uint8
import gmpy2 as gp
import cv2
imagearray = cv2.imread(r"C:\Users\gx\Downloads\picproblemd865943d\encflag.jpg")
h = len(imagearray)
w = len(imagearray[0])
y=1604145232044543633656616254647708451166351104281510395737885491696385806407267633308545985473789119651681711082023113933085624628557168423578747544761597312012713558891523798820667618256495398479378172124019360339427592449217208805888502769358288779859969965560832505104388955091637704481336716722418336373334467787371085728212260231330510705797124224353810509272250940285165605853594811893804251478850270703294638335268305881655491870226553141286503109543313414279220480589704210363277523457948607498351377843904335637032510420141505975997452077477296326035048463179997347136990808017374750824810458605412236391952910679246288287664717533857743462935708681309073915761377477454479206054016260422865457862565353002789887917196437750618212918420129464330488021272187952177063175896447842395209693304502304253471733746765257510395226972224876277717457205220726240042035259947453816668460757995771018155703600926745905595162857982860955545877343914746294034180707
x=1524993807674193841904821512553946379967374698278296055158206699585083472817489721493862711615915407326315660670541801753616900039772802728925226091475860689682871555641241500183892397513037971186709123629077584204226084524811673794984687840178772052545441242927492902583547355565525538664836516589721942980577095421561886873928634330640979800040574060218872787212426630202508118484269553983399179155489583316400107655564222453437462724749097265122300644936717434151331633092585140183510349369422527440264746843972834927860065578557836150798690530172694679514231722613822246810010130005324032492360889531553803832398604563088256410481865243771216990603166993198935358471831328395618477974126824762560872337594997394218234427050399655270848385995088586420526886397320949350980406936200217112040971433660322179072288438842964957568719036794320203116263329623589339367497303140938070334557345834226085189140858264388063745189833584962825509843279678826240558480527560
x1 = round(x/y*0.001, 16)
u1 = y*3650/x
x2 = round(x/y*0.00101, 16)
u2 = y*3675/x
x3 = round(x/y*0.00102, 16)
u3 = y*3680/x
kt = [x1, x2, x3]
temp_image = zeros(shape=[h, w, 3], dtype=uint8)
print(len(temp_image))
print(len(temp_image[0]))
print(len(temp_image[0][1]))
for k in range(0, 8):
    for i in range(0, h):
        for j in range(0, w):
            x1 = u1 * x1 * (1 - x1)
            x2 = u2 * x2 * (1 - x2)
            x3 = u3 * x3 * (1 - x3)
            r1 = int(x1*255)
            r2 = int(x2*255)
            r3 = int(x3*255)
            for t in range(0, 3):
                temp_image[i][j][t] = (imagearray[i][j][t]-((r1+r2) ^ r3)) % 256
    x1 = kt[0]
    x2 = kt[1]
    x3 = kt[2]
encflagarray = Image.fromarray(temp_image)
encflagarray.show()

1658112396513

太菜了 wo

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