数学但高中
x=4{0<y<6}
y=4{2<x<6,17<x<18,28<x<30,41<x<42}
y=6{4<x<6,15<x<16,17<x<19,41<x<43,50<x<51}
x=7{0<y<6}
(x-9)^2+(y-3)^2=1
x=10{2<y<3}
(x-12)^2+(y-3)^2=1
x=13{0<y<3}
y=0{11<x<13,15<x<16,50<x<51}
y=-x+17{14<x<15}
y=x-11{14<x<15}
x=15{0<y<2,4<y<6}
x=17{1<y<6}
x=19{3<y<4}
x=21{3<y<4}
(x-20)^2+(y-3)^2=1{2<y<3}
(x-23)^2+(y-3)^2=1{3<y<4}
x=22{2<y<3}
x=24{2<y<3}
(x-26)^2+(y-3)^2=1{25<x<26}
y=0.5x-11{26<x<27}
y=-0.5x+17{26<x<27}
y=2{29<x<30,31<x<33,39<x<40}
x=29{2<y<5}
x=32{2<y<5}
y=x-27{31<x<32}
(x-34)^2+((y-3.5)^2)/(1.5^2)=1
x=36{2<y<3}
(x-37)^2+(y-3)^2=1{3<y<4}
x=38{2<y<3}
x=41{2<y<6}
x=44{3<y<4}
(x-45)^2+(y-3)^2=1{2<y<3}
x=46{3<y<4}
x=47{2<y<3}
(x-48)^2+(y-3)^2=1{3<y<4}
x=49{2<y<3}
x=51{0<y<2,4<y<6}
y=x-49{51<x<52}
y=-x+55{51<x<52}
给了一堆式子，问了gpt才知道是作图，找个在线工具就行。
Simple_encryption
from Crypto.Util.number import *
import gmpy2
import random
import binascii
from secret import flag
p = getStrongPrime(1024)
q = getStrongPrime(1024)
N = p * q
g, r1, r2 = [getRandomRange(1, N) for _ in range(3)]
g1 = pow(g, r1 * (p - 1), N)
g2 = pow(g, r2 * (q - 1), N)
def encrypt(m):
s1, s2 = [getRandomRange(1, N) for _ in range(2)]
c1 = (m * pow(g1, s1, N)) % N
c2 = (m * pow(g2, s2, N)) % N
print("c1=", c1)
print("c2=", c2)
return (c1, c2)
c = encrypt(bytes_to_long(flag[:len(flag) // 2]))
print('N=', N)
print('g1=', g1)
def pad(msg, length):
l = len(msg)
return msg + (length - l) * chr(length - l).encode('utf-8')
p = getStrongPrime(1024)
q = getStrongPrime(1024)
assert (p != q)
n = p * q
e = 5
d = inverse(e, (p - 1) * (q - 1))
assert (e * d % (p - 1) * (q - 1))
flag = pad(flag[len(flag) // 2:], 48)
m = [int(binascii.b2a_hex(flag[i * 16:i * 16 + 16]).decode('utf-8'), 16) for i in range(3)]
print('S=', sum(m) % n)
cnt = len(m)
A = [(i + 128) ** 2 for i in range(cnt)]
B = [(i + 1024) for i in range(cnt)]
C = [(i + 512) for i in range(cnt)]
Cs = [int(pow((A[i] * m[i] ** 2 + B[i] * m[i] + C[i]), e, n)) for i in range(cnt)]
print('N=', n)
print('e=', e)
print('Cs=', Cs)
'''
c1= 19024563955839349902897822692180949371550067644378624199902067434708278125346234824900117853598997270022872667319428613147809325929092749312310446754419305096891122211944442338664613779595641268298482084259741784281927857614814220279055840825157115551456554287395502655358453270843601870807174309121367449335110327991187235786798374254470758957844690258594070043388827157981964323699747450405814713722613265012947852856714100237325256114904705539465145676960232769502207049858752573601516773952294218843901330100257234517481221811887136295727396712894842769582824157206825592614684804626241036297918244781918275524254
c2= 11387447548457075057390997630590504043679006922775566653728699416828036980076318372839900947303061300878930517069527835771992393657157069014534366482903388936689298175411163666849237525549902527846826224853407226289495201341719277080550962118551001246017511651688883675152554449310329664415179464488725227120033786305900106544217117526923607211746947511746335071162308591288281572603417532523345271340113176743703809868369623401559713179927002634217140206608963086656140258643119596968929437114459557916757824682496866029297120246221557017875892921591955181714167913310050483382235498906247018171409256534124073270350
N= 21831630625212912450058787218272832615084640356500740162478776482071876178684642739065105728423872548532056206845637492058465613779973193354996353323494373418215019445325632104575415991984764454753263189235376127871742444636236132111097548997063091478794422370043984009615893441148901566420508196170556189546911391716595983110030778046242014896752388438535131806524968952947016059907135882390507706966746973544598457963945671064540465259211834751973065197550500334726779434679470160463944292619173904064826217284899341554269864669620477774678605962276256707036721407638013951236957603286867871199275024050690034901963
g1= 20303501619435729000675510820217420636246553663472832286487504757515586157679361170332171306491820918722752848685645096611030558245362578422584797889428493611704976472409942840368080016946977234874471779189922713887914075985648876516896823599078349725871578446532134614410886658001724864915073768678394238725788245439086601955497248593286832679485832319756671985505398841701463782272300202981842733576006152153012355980197830911700112001441621619417349747262257225469106511527467526286661082010163334100555372381681421874165851063816598907314117035131618062582953512203870615406642787786668571083042463072230605649134
S= 234626762558445335519229319778735528295
N= 28053749721930780797243137464055357921262616541619976645795810707701031602793034889886420385567169222962145128498131170577184276590698976531070900776293344109534005057067680663813430093397821366071365221453788763262381958185404224319153945950416725302184077952893435265051402645871699132910860011753502307815457636525137171681463817731190311682277171396235160056504317959832747279317829283601814707551094074778796108136141845755357784361312469124392408642823375413433759572121658646203123677327551421440655322226192031542368496829102050186550793124020718643243789525477209493783347317576783265671566724068427349961101
e= 5
Cs= [1693447496400753735762426750097282582203894511485112615865753001679557182840033040705025720548835476996498244081423052953952745813186793687790496086492136043098444304128963237489862776988389256298142843070384268907160020751319313970887199939345096232529143204442168808703063568295924663998456534264361495136412078324133263733409362366768460625508816378362979251599475109499727808021609000751360638976, 2240772849203381534975484679127982642973364801722576637731411892969654368457130801503103210570803728830063876118483596474389109772469014349453490395147031665061733965097301661933389406031214242680246638201663845183194937353509302694926811282026475913703306789097162693368337210584494881249909346643289510493724709324540062077619696056842225526183938442535866325407085768724148771697260859350213678910949, 5082341111246153817896279104775187112534431783418388292800705085458704665057344175657566751627976149342406406594179073777431676597641200321859622633948317181914562670909686170531929552301852027606377778515019377168677204310642500744387041601260593120417053741977533047412729373182842984761689443959266049421034949822673159561609487404082536872314636928727833394518122974630386280495027169465342976]
'''
前半部分：
- $N = p \cdot q$
- $g1 = g^{r_1\cdot (p-1)} mod N$
- $g2 = g^{r_2\cdot (q-1)} mod N$
费马定理：
- $g1 = 1 mod N$
- $g2 = 1 mod N$
故$p = gcd(g1-1,N)$
前一半flag：
- $c1= m\cdot g_1^{s_1} mod N$
- $c2= m\cdot g_2^{s_2} mod N$
$N、g1、c1、c2已知$
带入$g1$和$g2$，再次用费马小定理：
- $c1 = m mod p$
- $c2 = m mod q$
$m1 = c1 mod p$
后半部分：
m 是一个包含三个整数的列表，它们分别对应着原始 flag 的前 16 字节、第 17 到 32 字节、以及第 33 到 48 字节。
$A = [16384, 16641, 16900],B = [1024, 1025, 1026], C = [512, 513, 514]$
Cs = [int(pow((A[i] * m[i] ** 2 + B[i] * m[i] + C[i]), e, n)) for i in range(cnt)]
$CS[i] = (A[i]\cdot m[i]^{2} + B[i] \cdot m[i]+C[i])^e mod n$
仅含未知数m[i]，sage解方程求出m：
m = [65413472431888815878902893901773169457,133183392452574799979498526266539842331, 36029897673981719660827899610422516507]
print(long_to_bytes(m[0])+long_to_bytes(m[1]))
#b'16-18fa-ec795fc1d208}\x1b\x1b\x1b\x1b\x1b\x1b\x1b\x1b\x1b\x1b\x1b'
#后面是填充的部分
后一半flag也有了
Rosita
# Problem by rec, without any sleep at all.
from Crypto.Util.number import bytes_to_long as b2l
from hashlib import sha256
from os import urandom
from secret import p, a, b, flag
ECC = EllipticCurve(GF(p), [a, b])
R, E, C = [ECC.random_point() for _ in range(3)]
pad = lambda m: urandom(8) + m + b'\x00' * (ZZ(p).nbits() // 8 - len(m) - 8 - 1)
out = list()
for i in range(len(flag)):
m = pad(chr(flag[i]).encode())
nonce = urandom(16)
sh = sha256(nonce + m).digest()
Q = b2l(m)*R + b2l(nonce)*E + b2l(sh)*C
out.append(Q.xy())
with open('out.tuo', 'w') as f:
f.write(str(out))
有点难理解，把佬的wp先放着：
2023巅峰极客 Crypto Rosita - L00kback - 博客园 (cnblogs.com)
(25条消息) 巅峰极客2023 Crypto Rosita_无趣的浅的博客-CSDN博客
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