ACTF 2023 部分WP-Toy模板网

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来自密码手的哀嚎：

玩不了一点，太难了。

CRYPTO

MDH

Description

Malin’s Diffile-Hellman Key Exchange.

task.sage

from hashlib import sha256
from secret import flag

r = 128
c = 96
p = 308955606868885551120230861462612873078105583047156930179459717798715109629
Fp = GF(p)

def gen():
    a1 = random_matrix(Fp, r, c)
    a2 = random_matrix(Fp, r, c)
    A = a1 * a2.T
    return (a1, a2), A

sk_alice, pk_alice = gen()
sk_bob, pk_bob = gen()
shared = (sk_alice[0].T * pk_bob * sk_alice[1]).trace()
ct = int(sha256(str(int(shared)).encode()).hexdigest(), 16) ^^ int.from_bytes(flag, 'big')

with open('output.txt', 'wb') as f:
    f.write(str(ct).encode() + b'\n')
    f.write(str(list(pk_alice)).encode() + b'\n')
    f.write(str(list(pk_bob)).encode() + b'\n')

output.txt

8308943029741424587523612386337754255889681699670071706719724435165094611096603769021839263
[(248911473252706126701034292146541373251616513930062195044617795903221826522, 2006663512374471656012713476848952481708164609054161957903243961884729327, 34477445744870695124522330116853976140397756578144976256418933561356297270, 134510431748375978099734325290614896206741166021565864231628975299374894934, 263052897010932566643732419798564392599203662525075356313352360336696893126, 141993015830421728697942660480086149608207938704594224742919997457007731362, 2884941569385999952542152446419918040970038754772386008722345958209977361, 251929132317823958330447233877195880589103297101688031807949769646459583779, 202402171486986340762120037260332866100215659317408872569460852300216859639, 299869910419680584431600458234987314403629236129755735947187138970557973965, 32123365781587714822724172153965985134547746672138349976513502380627017939,........

分析一下：

shared = (sk_alice[0].T * pk_bob * sk_alice[1]).trace()

也就是说shared = （（a₁)^T * b₁* (b₂)^T * a₂ ）.trace()

已知Pk_alice = a₁ * (a₂)^T和Pk_bob = b₁* (b₂)^T

线性代数学的好的我们可以根据矩阵的迹的性质：Tr(A) = Tr(A^T) ,Tr(AB) = Tr(BA)

因此我们可以把shared 内容交换下顺序得到 shared = （（a₁)^T * a₂ * (b₂)^T * b₁）.trace()

即shared = (Pk_alice.T * Pk_bob).trace()

exp:

from hashlib import sha256

p = 308955606868885551120230861462612873078105583047156930179459717798715109629
Fq = GF(p)

f = open("output.txt",'r')
data = f.readlines()

ct = eval(data[0])
pk_alice = eval(data[1])
pk_bob = eval(data[2])

pk_alice = Matrix(Fp,pk_alice)
pk_bob = Matrix(Fq,pk_bob)

shared = (pk_alice.T * pk_bob).trace()

m = int(sha256(str(int(shared)).encode()).hexdigest(), 16) ^^ ct
flag = bytes.fromhex(hex(m)[2:])
print(flag)
# ACTF{do_you_know_f0rm2l1n_1s_4w3s0m3!}

EasyRSA

Description

EasyRSA

from secret import flag
from Crypto.Util.number import *


def genKey(nbits, dbits):
    bbits = (nbits // 2 - dbits) // 2

    while True:
        a = getRandomNBitInteger(dbits)
        b = getRandomNBitInteger(bbits)
        c = getRandomNBitInteger(bbits)
        p1 = a * b * c + 1
        if isPrime(p1):
            # print("p1 =", p1)
            break

    while True:
        d = getRandomNBitInteger(dbits)
        p2 = b * c * d + 1
        if isPrime(p2):
            # print("p2 =", p2)
            break

    while True:
        e = getRandomNBitInteger(bbits)
        f = getRandomNBitInteger(bbits)
        q1 = e * d * f + 1
        p3 = a * e * f + 1
        if isPrime(q1) and isPrime(p3):
            # print("p3 =", p3)
            # print("q1 =", q1)
            break

    while True:
        d_ = getRandomNBitInteger(dbits)
        if GCD(a * b * c * d * e * f, d_) != 1:
            continue
        e_ = inverse(d_, a * b * c * d * e * f)
        k1 = (e_ * d_ - 1) // (a * b * c * d * e * f)
        assert e_ * d_ == (a * b * c * d * e * f) * k1 + 1
        q2 = k1 * e * f + 1
        q3 = k1 * b * c + 1
        if isPrime(q2) and isPrime(q3):
            # print("q2 =", q2)
            # print("q3 =", q3)
            # print("e =", e_)
            # print("d =", d_)
            break

    n1 = p1 * q1
    n2 = p2 * q2
    n3 = p3 * q3
    
    assert pow(pow(0xdeadbeef, e_, n1), d_, n1) == 0xdeadbeef
    assert pow(pow(0xdeadbeef, e_, n2), d_, n2) == 0xdeadbeef
    assert pow(pow(0xdeadbeef, e_, n3), d_, n3) == 0xdeadbeef

    return(e_, n1, n2, n3)


nbits = 0x600
dbits = 0x210

m = bytes_to_long(flag)
e, n1, n2, n3 = genKey(nbits, dbits)
c = pow(m, e, n1)

print("c =", c)
print("e =", e)
print("n1 =", n1)
print("n2 =", n2)
print("n3 =", n3)

# c = 63442255298812942222810837512019302954917822996915527697525497640413662503768308023517128481053593562877494934841788054865410798751447333551319775025362132176942795107214528962480350398519459474033659025815248579631003928932688495682277210240277909527931445899728273182691941548330126199931886748296031014210795428593631253184315074234352536885430181103986084755140024577780815130067722355861473639612699372152970688687877075365330095265612016350599320999156644
# e = 272785315258275494478303901715994595013215169713087273945370833673873860340153367010424559026764907254821416435761617347240970711252213646287464416524071944646705551816941437389777294159359383356817408302841561284559712640940354294840597133394851851877857751302209309529938795265777557840238332937938235024502686737802184255165075195042860413556866222562167425361146312096189555572705076252573222261842045286782816083933952875990572937346408235562417656218440227
# n1 = 473173031410877037287927970398347001343136400938581274026578368211539730987889738033351265663756061524526288423355193643110804217683860550767181983527932872361546531994961481442866335447011683462904976896894011884907968495626837219900141842587071512040734664898328709989285205714628355052565784162841441867556282849760230635164284802614010844226671736675222842060257156860013384955769045790763119616939897544697150710631300004180868397245728064351907334273953201
# n2 = 327163771871802208683424470007561712270872666244394076667663345333853591836596054597471607916850284565474732679392694515656845653581599800514388800663813830528483334021178531162556250468743461443904645773493383915711571062775922446922917130005772040139744330987272549252540089872170217864935146429898458644025927741607569303966038195226388964722300472005107075179204987774627759625183739199425329481632596633992804636690274844290983438078815836605603147141262181
# n3 = 442893163857502334109676162774199722362644200933618691728267162172376730137502879609506615568680508257973678725536472848428042122350184530077765734033425406055810373669798840851851090476687785235612051747082232947418290952863499263547598032467577778461061567081620676910480684540883879257518083587862219344609851852177109722186714811329766477552794034774928983660538381764930765795290189612024799300768559485810526074992569676241537503405494203262336327709010421

参考：https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4276937

分析如下：

ACTF 2023 部分WP

于是有：

ACTF 2023 部分WP

构造格:

ACTF 2023 部分WP

调至平衡后，LLL即可得d，exp：

ACTF 2023 部分WP

#Sage#
from gmpy2 import *
c = 63442255298812942222810837512019302954917822996915527697525497640413662503768308023517128481053593562877494934841788054865410798751447333551319775025362132176942795107214528962480350398519459474033659025815248579631003928932688495682277210240277909527931445899728273182691941548330126199931886748296031014210795428593631253184315074234352536885430181103986084755140024577780815130067722355861473639612699372152970688687877075365330095265612016350599320999156644
e_ = 272785315258275494478303901715994595013215169713087273945370833673873860340153367010424559026764907254821416435761617347240970711252213646287464416524071944646705551816941437389777294159359383356817408302841561284559712640940354294840597133394851851877857751302209309529938795265777557840238332937938235024502686737802184255165075195042860413556866222562167425361146312096189555572705076252573222261842045286782816083933952875990572937346408235562417656218440227
n1 = 327163771871802208683424470007561712270872666244394076667663345333853591836596054597471607916850284565474732679392694515656845653581599800514388800663813830528483334021178531162556250468743461443904645773493383915711571062775922446922917130005772040139744330987272549252540089872170217864935146429898458644025927741607569303966038195226388964722300472005107075179204987774627759625183739199425329481632596633992804636690274844290983438078815836605603147141262181
n2 = 442893163857502334109676162774199722362644200933618691728267162172376730137502879609506615568680508257973678725536472848428042122350184530077765734033425406055810373669798840851851090476687785235612051747082232947418290952863499263547598032467577778461061567081620676910480684540883879257518083587862219344609851852177109722186714811329766477552794034774928983660538381764930765795290189612024799300768559485810526074992569676241537503405494203262336327709010421
n3 = 473173031410877037287927970398347001343136400938581274026578368211539730987889738033351265663756061524526288423355193643110804217683860550767181983527932872361546531994961481442866335447011683462904976896894011884907968495626837219900141842587071512040734664898328709989285205714628355052565784162841441867556282849760230635164284802614010844226671736675222842060257156860013384955769045790763119616939897544697150710631300004180868397245728064351907334273953201

assert n1<n2<n3
M=iroot(int(n3),int(2))[0]
a=[0]*4
a[0]=[M,e_,e_,e_]
a[1]=[0,-n1,0,0]
a[2]=[0,0,-n2,0]
a[3]=[0,0,0,-n3]

Mat = matrix(ZZ,a)
Mat_LLL=Mat.LLL()
# Mat_LLL
assert abs(Mat_LLL[0][0])%M == 0
d = abs(Mat_LLL[0][0])//M
m = int(pow(c,d,n3))
print(m)
#35686638577043308509433001447876425162918967675752639038862176644952428441723169894674809981369528957

from Crypto.Util.number import long_to_bytes
m = 35686638577043308509433001447876425162918967675752639038862176644952428441723169894674809981369528957
print('💌:',long_to_bytes(m))
#💌: b'ACTF{5FFC427B-F14F-DCA0-C425-675B149890C2}'

MidRSA

Description

MidRSA

from secret import flag
from Crypto.Util.number import *


def genKey(nbits, dbits):
    bbits = (nbits // 2 - dbits) // 2

    while True:
        a = getRandomNBitInteger(dbits)
        b = getRandomNBitInteger(bbits)
        c = getRandomNBitInteger(bbits)
        p1 = a * b * c + 1
        if isPrime(p1):
            # print("p1 =", p1)
            break

    while True:
        d = getRandomNBitInteger(dbits)
        p2 = b * c * d + 1
        if isPrime(p2):
            # print("p2 =", p2)
            break

    while True:
        e = getRandomNBitInteger(bbits)
        f = getRandomNBitInteger(bbits)
        q1 = e * d * f + 1
        p3 = a * e * f + 1
        if isPrime(q1) and isPrime(p3):
            # print("p3 =", p3)
            # print("q1 =", q1)
            break

    while True:
        d_ = getRandomNBitInteger(dbits)
        if GCD(a * b * c * d * e * f, d_) != 1:
            continue
        e_ = inverse(d_, a * b * c * d * e * f)
        k1 = (e_ * d_ - 1) // (a * b * c * d * e * f)
        assert e_ * d_ == (a * b * c * d * e * f) * k1 + 1
        q2 = k1 * e * f + 1
        q3 = k1 * b * c + 1
        if isPrime(q2) and isPrime(q3):
            # print("q2 =", q2)
            # print("q3 =", q3)
            # print("e =", e_)
            print("d =", d_)
            break

    n1 = p1 * q1
    n2 = p2 * q2
    n3 = p3 * q3
    
    assert pow(pow(0xdeadbeef, e_, n1), d_, n1) == 0xdeadbeef
    assert pow(pow(0xdeadbeef, e_, n2), d_, n2) == 0xdeadbeef
    assert pow(pow(0xdeadbeef, e_, n3), d_, n3) == 0xdeadbeef

    return(e_, n1, n2, n3)


nbits = 0x600
dbits = 0x240

m = bytes_to_long(flag)
e, n1, n2, n3 = genKey(nbits, dbits)
c = pow(m, e, n1)

print("c =", c)
print("e =", e)
print("n1 =", n1)
print("n2 =", n2)
print("n3 =", n3)


# c = 598823083137858565473505718525815255620672892612784824187302545127574115000325539999824374357957135208478070797113625659118825530731575573239221853507638809719397849963861367352055486212696958923800593172417262351719477530809870735637329898331854130533160020420263724619225174940214193740379571953951059401685115164634005411478583529751890781498407518739069969017597521632392997743956791839564573371955246955738575593780508817401390102856295102225132502636316844
# e = 334726528702628887205076146544909357751287869200972341824248480332256143541098971600873722567713812425364296038771650383962046800505086167635487091757206238206029361844181642521606953049529231154613145553220809927001722518303114599682529196697410089598230645579658906203453435640824934159645602447676974027474924465177723434855318446073578465621382859962701578350462059764095163424218813852195709023435581237538699769359084386399099644884006684995755938605201771
# n1 = 621786427956510577894657745225233425730501124908354697121702414978035232119311662357181409283130180887720760732555757426221953950475736078765267856308595870951635246720750862259255389006679454647170476427262240270915881126875224574474706572728931213060252787326765271752969318854360970801540289807965575654629288558728966771231501959974533484678236051025940684114262451777094234017210230731492336480895879764397821363102224085859281971513276968559080593778873231
# n2 = 335133378611627373902246132362791381335635839627660359611198202073307340179794138179041524058800936207811546752188713855950891460382258433727589232119735602364790267515558352318957355100518427499530387075144776790492766973547088838586041648900788325902589777445641895775357091753360428198189998860317775077739054298868885308909495601041757108114540069950359802851809227248145281594107487276003206931533768902437356652676341735882783415106786497390475670647453821
# n3 = 220290953009399899705676642623181513318918775662713704923101352853965768389363281894663344270979715555659079125651553079702318700200824118622766698792556506368153467944348604006011828780474050012010677204862020009069971864222175380878120025727369117819196954091417740367068284457817961773989542151049465711430065838517386380261817772422927774945414543880659243592749932727798690742051285364898081188510009069286094647222933710799481899960520270189522155672272451

改写等式，爆破d_低16位，构建格求解。

对于

ACTF 2023 部分WP

有

ACTF 2023 部分WP

构造格：

ACTF 2023 部分WP

调至平衡后，LLL求得d的高位

然后拼接d的低位后，即恢复d，exp:

#Sage#
from gmpy2 import *
from tqdm import tqdm
from Crypto.Util.number import *


c = 598823083137858565473505718525815255620672892612784824187302545127574115000325539999824374357957135208478070797113625659118825530731575573239221853507638809719397849963861367352055486212696958923800593172417262351719477530809870735637329898331854130533160020420263724619225174940214193740379571953951059401685115164634005411478583529751890781498407518739069969017597521632392997743956791839564573371955246955738575593780508817401390102856295102225132502636316844
e_ = 334726528702628887205076146544909357751287869200972341824248480332256143541098971600873722567713812425364296038771650383962046800505086167635487091757206238206029361844181642521606953049529231154613145553220809927001722518303114599682529196697410089598230645579658906203453435640824934159645602447676974027474924465177723434855318446073578465621382859962701578350462059764095163424218813852195709023435581237538699769359084386399099644884006684995755938605201771
n3 = 621786427956510577894657745225233425730501124908354697121702414978035232119311662357181409283130180887720760732555757426221953950475736078765267856308595870951635246720750862259255389006679454647170476427262240270915881126875224574474706572728931213060252787326765271752969318854360970801540289807965575654629288558728966771231501959974533484678236051025940684114262451777094234017210230731492336480895879764397821363102224085859281971513276968559080593778873231
n2 = 335133378611627373902246132362791381335635839627660359611198202073307340179794138179041524058800936207811546752188713855950891460382258433727589232119735602364790267515558352318957355100518427499530387075144776790492766973547088838586041648900788325902589777445641895775357091753360428198189998860317775077739054298868885308909495601041757108114540069950359802851809227248145281594107487276003206931533768902437356652676341735882783415106786497390475670647453821
n1 = 220290953009399899705676642623181513318918775662713704923101352853965768389363281894663344270979715555659079125651553079702318700200824118622766698792556506368153467944348604006011828780474050012010677204862020009069971864222175380878120025727369117819196954091417740367068284457817961773989542151049465711430065838517386380261817772422927774945414543880659243592749932727798690742051285364898081188510009069286094647222933710799481899960520270189522155672272451

n1,n2,n3 = sorted([n1,n2,n3])

assert n1<n2<n3

def solve():

    for dl in tqdm(range(2^16)):
        a=[0]*5
        a[0]=[2^(16+767),e_*2^16,e_*2^16,e_*2^16,0]
        a[1]=[0,-n1,0,0,0]
        a[2]=[0,0,-n2,0,0]
        a[3]=[0,0,0,-n3,0]
        a[4]=[0,e_*dl,e_*dl,e_*dl,2^(576+767)]

        Mat = matrix(ZZ,a)
        Mat_LLL=Mat.LLL()

        for line in Mat_LLL:
            if (abs(line[-1]) == 2^(576+767)):
                dh = abs(line[0])//2^(16+767)
                d = int((dh<<16)+dl)

                m = int(pow(c,d,n1))
                flag1 = long_to_bytes(m)

                m = int(pow(c,d,n2))
                flag2 = long_to_bytes(m)

                m = int(pow(c,d,n3))
                flag3 = long_to_bytes(m)

                flags = [flag1, flag2,flag3]
                for f in flags:
                    if b'ACTF{' in f:
                        print(f)
                        return
solve()  # ACTF{D16C46D9-77A2-2D96-CA51-4538EFB6AFF7}

claw crane

Description

抓娃娃咯 / Grabbing Dolls

Service

Access via

nc 152.136.172.227 22222

文章来源地址https://www.toymoban.com/news/detail-736282.html

查看代码

 #!/usr/bin/env python3
from Crypto.Util.number import (
    bytes_to_long, long_to_bytes
)
from hashlib import md5
import os, signal
import sys
import random

BITS = 128

class ClawCrane(object):
    def __init__(self) -> None:
        self.seed = bytes_to_long(os.urandom(BITS//8))
        self.bless = 0
        self.score = 0
    
    def get_input(self, prompt="> "):
        print(prompt, end="")
        sys.stdout.flush()
        return input()
    
    def check_pos(self, pos, moves):
        col, row = 0, 0
        for move in moves:
            if move == "W":
                if row < 15: row += 1
            elif move == "S":
                if row > 0: row -= 1
            elif move == "A":
                if col > 0: col -= 1
            elif move == "D":
                if col < 15: col += 1
            else:
                return -1
        print(col, row)
        return pos == [col, row]
    
    def gen_chaos(self, inp):
        def mapping(x):
            if x=='W': return "0"
            if x=='S': return "1"
            if x=='A': return "2"
            if x=='D': return "3"
        vs = int("".join(map(mapping, inp)), 4)
        chaos = bytes_to_long(md5(
                    long_to_bytes((self.seed + vs) % pow(2,BITS))
                ).digest())
        self.seed = (self.seed + chaos + 1) % pow(2,BITS)
        return chaos
    
    def destiny_claw(self, delta):
        bits = bin(delta)[2:]
        if len(bits) < 128+self.bless:
            bits += "0"*(128+self.bless - len(bits))
        c = random.choice(bits)
        if c=='0': return True
        else: return False
    
    def run(self):
        pos = [random.randrange(1,16), random.randrange(1,16)]
        moves = self.get_input(f"i am at {pos}, claw me.\nYour moves: ")
        if len(moves) > 100:
            print("too many steps")
            return
        if not self.check_pos(pos, moves):
            print("sorry, clawed nothing")
            return
        r = self.gen_chaos(moves[:64])
        print(f"choas: {r}")
        p, q = map(int, self.get_input(f"give me your claw using p,q and p,q in [0, 18446744073709551615] (e.g.: 1,1): ").split(","))
        if not (p>0 and p<pow(2,BITS//2) and q>0 and q<pow(2,BITS//2)):
            print("not in range")
            return
        delta = abs(r*q - p*pow(2,BITS))
        if self.destiny_claw(delta):
            self.score += 10
            self.bless = 0
            print("you clawed it")
        else:
            self.bless += 16
            print("sorry, clawed nothing")

import hashlib
import os

def generate_proof_of_work(size,difficulty):
    target = os.urandom(size).hex()
    hash_value = hashlib.sha1(target.encode()).hexdigest()
    return target[difficulty:],hash_value

def check_proof_of_work(prefix,suffix,expected):
    return hashlib.sha1(f'{prefix}{suffix}'.encode()).hexdigest()==expected

def proof():
    POW_SIZE=32
    POW_DIFFICULTY=6
    suff,hs=generate_proof_of_work(POW_SIZE,POW_DIFFICULTY)
    print(f'sha1(prefix+"{suff}")=={hs}')
    pref=input("prefix = ?\n")
    if not check_proof_of_work(pref,suff,hs):
        print("PoW error")
        exit(1)

def main():
    signal.alarm(600)
    proof()
    cc = ClawCrane()
    for _ in range(256):
        try:
            cc.run()
            print(f"your score: {cc.score}")
        except:
            print(f"abort")
            break
    if cc.score >= 2220:
        print(f"flag: {open('/flag.txt').read()}")
        
if __name__ == "__main__":
    main()

题目的终极目标是拿到2220分，即256次交互至少有222次得分，是个相当大的概率。

第一想法有两个：

一个是在34次交互内拿到某个必要条件（比如seed值）以达成题目通过。

另一个是利用某种办法控制通关概率在相当高的水平，跑几次脚本通关。

那么在开始得分前，我们简单分析流程，首先得把它的得分步骤给搞清楚。

题目给出一个坐标，并且要求我们在100次移动内从0,0位置移动到目标坐标，移动字符串使用AWSD进行表示，如果移动指令没能成功完成移动操作，那么这次交互机会就会被浪费。

def check_pos(self, pos, moves):
        col, row = 0, 0
        for move in moves:
            if move == "W":
                if row < 15: row += 1
            elif move == "S":
                if row > 0: row -= 1
            elif move == "A":
                if col > 0: col -= 1
            elif move == "D":
                if col < 15: col += 1
            else:
                return -1
        print(col, row)
        return pos == [col, row]

这个字符串在编码成数字以后，直接影响到随机种子的前进。

def gen_chaos(self, inp):
        def mapping(x):
            if x=='W': return "0"
            if x=='S': return "1"
            if x=='A': return "2"
            if x=='D': return "3"
        vs = int("".join(map(mapping, inp)), 4)
        chaos = bytes_to_long(md5(
                    long_to_bytes((self.seed + vs) % pow(2,BITS))
                ).digest())
        self.seed = (self.seed + chaos + 1) % pow(2,BITS)
        return chaos

r = self.gen_chaos(moves[:64])

看到这里的想法是chaos是能够被操控利用的，我们可以在move的前64bit填上任意的移动方式来控制vs的值，比如我们控制第一个vs为0，前一次的chaos操作让它满足seed1 = seed0+chaos+1，chaos已知，那么这时候我们令vs1+chaos+1 = 2^128，就能够令chaos1 = md5(seed）=chaos，有seed2 = seed1+chaos+1+chaos1+1，再令vs2+（chaos+1+chaos1+1） = 2^128.....这样我们就能够永远控制输出的chaos为一个相同的值。

而chaos相同的用处很显然就来自于可以影响最后抽奖的结果。现在只要我们能够找到一组数据，使delta中0的部分占比很大，就能够完成这个问题的求解。

r = self.gen_chaos(moves[:64])
        print(f"choas: {r}")
        p, q = map(int, self.get_input(f"give me your claw using p,q and p,q in [0, 18446744073709551615] (e.g.: 1,1): ").split(","))
        if not (p>0 and p<pow(2,BITS//2) and q>0 and q<pow(2,BITS//2)):
            print("not in range")
            return
        delta = abs(r*q - p*pow(2,BITS))
        if self.destiny_claw(delta):
            self.score += 10
            self.bless = 0
            print("you clawed it")
        else:
            self.bless += 16
            print("sorry, clawed nothing")

p和q是我们自己构造的(0,2^64)之间的数字，我们生成一个rq-p2^128形式的数字（也可以理解为在操作rq%2^128)，如果在二进制中抽奖抽到0，则进行加分。如果我们要在256次判定中得到222次成功，最好需要保证128个二进制位中有111个0，这里可能需要捏个格去进行求解。所以我们使用了一个基础的格子，求解得到64bit的短向量delta,p，在p为小参数的同时，q一定也为小参数。

from hashlib import sha256,md5
from pwn import *
context.log_level = 'debug'
import re
import gmpy2
import libnum

p = remote('152.136.172.227',22222)

def num2awds(num):
    mov_abt = 'WSAD'
    aim = ''

    for i in range(128):
        aim = mov_abt[num%4] + aim
        num //= 4
        
    return aim

def mov_construct(end,head):
    xend,yend = end
    x,y = 0,0
    for i in head:
        if i == 'W':
            if y < 15: y += 1
        elif i == 'S':
            if y > 0: y -= 1
        elif i == 'A':
            if x > 0: x -= 1
        elif i == 'D':
            if x < 15: x += 1
    if x > xend:
        for i in range(x-xend):
            head += 'A'
    else:
        for i in range(xend-x):
            head += 'D'
    if y > yend:
        for i in range(y-yend):
            head += 'S'
    else:
        for i in range(yend-y):
            head += 'W'
    return head


for i in range(256):
    a = p.recvline().decode()
    a = a.split(' ')
    x,y = int(a[3][1:-1]),int(a[4][:-2])
    p.recvuntil(b'Your moves: ')
    p.sendline(mov_construct((x,y),'W'*64).encode())
    p.recvline()
    chaos = int(p.recvline()[7:].decode())
    p.recvuntil(b'(e.g.: 1,1): ')
    p.sendline(b'1,2')
    p.recvuntil(b'your score:')
    p.recvline()

普通跑一轮是1410，接下来固定r试试，固定r+格64，可以打到2020，还差200分。目前这个脚本大概是稳1800，我感觉直接LLL不是求出最少1的最好的方法，可能还得往上做改进。

from hashlib import sha256,md5
from pwn import *
context.log_level = 'debug'
import re
import gmpy2
import libnum

p = remote('152.136.172.227',22222)

def num2awds(num):
    mov_abt = 'WSAD'
    aim = ''
    
    for i in range(64):
        aim = mov_abt[num%4] + aim
        num //= 4
        
    return aim

def mov_construct(end,head):
    xend,yend = end
    x,y = 0,0
    for i in head:
        if i == 'W':
            if y < 15: y += 1
        elif i == 'S':
            if y > 0: y -= 1
        elif i == 'A':
            if x > 0: x -= 1
        elif i == 'D':
            if x < 15: x += 1
    if x > xend:
        for i in range(x-xend):
            head += 'A'
    else:
        for i in range(xend-x):
            head += 'D'
    if y > yend:
        for i in range(y-yend):
            head += 'S'
    else:
        for i in range(yend-y):
            head += 'W'
    return head


a = p.recvline().decode()
a = a.split(' ')
x,y = int(a[3][1:-1]),int(a[4][:-2])
p.recvuntil(b'Your moves: ')
p.sendline(mov_construct((x,y),'W'*64).encode())
p.recvline()
chaos = int(p.recvline()[7:].decode())
tmp = chaos+1
print(tmp)
p.recvuntil(b'(e.g.: 1,1): ')
p.sendline(b'1,2')
p.recvuntil(b'your score:')
p.recvline()

P,Q = int(input()),int(input())
    
for i in range(256):
    a = p.recvline().decode()
    a = a.split(' ')
    x,y = int(a[3][1:-1]),int(a[4][:-2])
    p.recvuntil(b'Your moves: ')
    cnum = int((-tmp)%2**128)
    print('cnum:',cnum)
    p.sendline(mov_construct((x,y),num2awds(cnum)).encode())
    p.recvline()
    chaos = int(p.recvline()[7:].decode())
    tmp += chaos+1
    p.recvuntil(b'(e.g.: 1,1): ')
    p.sendline(f'{P},{Q}'.encode())
    p.recvuntil(b'your score:')
    p.recvline()

a = 239996570097549520897992758078844507254
b = 2^128

m = matrix([[a,1],[b,0]])

print(m.LLL())

p = 8750581204523477797
q = (a*p-22959585545265104654)/b
print(q)

print(a*p-b*q)

ACTF 2023 部分WP

找到新窍门！令结果为负值，q加一个2^63就会形成这种效果（得保证在界内）：

-0b100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010100101100101100010011110001100011010000100110011110010110110

if len(bits) < 128+self.bless:
            bits += "0"*(128+self.bless - len(bits))

把长度拉伸至192，这样题目zfill的128就变成了192，从而通过改变字长来达到提高正确率的效果，相当于自带了4次bless。跑几遍脚本就可以拿到一组通过2220的数据。

a = 182169930054624761546696716074077090774
b = 2^128

m = matrix([[a,1],[b,0]])

print(m.LLL())

p = 6207226441042315485
print(p > 2^64)
q = (a*p+10341573661598863426)/b

print(q+2^63)
print((q+2^63 ) > 2^64)

MISC

SIGNIN: 东方原神大学（签到题）

Description

1944 年，英国剑桥大学著名生物化学家李约瑟来到浙江大学，并盛赞浙江大学是“东方剑桥”，浙大也通过矢志不渝的发展和进步，证明了自己的含金量。

2020 年，开放冒险游戏原神横空出世，世界各地的游戏玩家都被这个具有宏大世界观并蕴含丰富中华传统文化的佳作所吸引，就连 AAA 战队的指导老师 BlackWhite 都赞其颇有塞尔达之神韵。

在接下来的几年间，各大高校间兴起了一阵原神大学之风，中国石油大学轻添寥寥数笔，便将自己的校名改为了中国原神大学，而哈尔滨工业大学也接下了建设提瓦特工业大学的光荣使命，众多学校也进入了原神大学称号的抢夺战之中。然而，~~作为全国排名第三的大学~~，浙江大学还没有自己的原神大学称号。这时浙江大学 AAA 的队员们想起了李约瑟对浙大“东方剑桥”的盛赞，恍然大悟，浙江大学不就是东方原神大学吗！

所以，欢迎来到东方提瓦特大陆