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2019SCTF-Writeup /

作者：De1ta
題目首先需要proof_of_work，要求m和rsa加密m之后再解密的結果不相同，讓m比n大即可繞過

進入系統之后有兩個選項

1.隨機生成三組不同的a，b，n，使用相同的e=3，使得c=pow(a*m+b,e,n)，然后會給我們三組不同的a，b，n和c。最后再使用aes_ofb加密m，將結果也給我們。其中aes的iv和key都是隨機生成的

2.我們需要輸入aes_ofb加密之后的m的結果，其中m需要將其中的afternoon替換為morning，如果構造的正確則返回flag 解題思路：

1.通過Broadcast Attack with Linear Padding解出m為”I will send you the ticket tomorrow afternoon”

2.將m，修改后的m，以及aes_ofb加密之后的m的結果進行異或，得到的最終結果就是修改后的m進行aes_ofb加密之后的結果。將此結果發送給服務器便得到flag

sctf{7h15_ch4ll3n63_15_n07_h4rd_f0r_y0u_r16h7?}

解題腳本:

1.hastads.sage

def hastads(cArray,nArray,e=3):
    """
    Performs Hastads attack on raw RSA with no padding.
    cArray = Ciphertext Array
    nArray = Modulus Array
    e = public exponent
    """

    if(len(cArray)==len(nArray)==e):
        for i in range(e):
            cArray[i] = Integer(cArray[i])
            nArray[i] = Integer(nArray[i])
        M = crt(cArray,nArray)
        return(Integer(M).nth_root(e,truncate_mode=1))
    else:
        print("CiphertextArray, ModulusArray, need to be of the same length, and the same size as the public exponent")


def linearPaddingHastads(cArray,nArray,aArray,bArray,e=3,eps=1/8):
    """
    Performs Hastads attack on raw RSA with no padding.
    This is for RSA encryptions of the form: cArray[i] = pow(aArray[i]*msg + bArray[i],e,nArray[i])
    Where they are all encryptions of the same message.
    cArray = Ciphertext Array
    nArray = Modulus Array
    aArray = Array of 'slopes' for the linear padding
    bArray = Array of 'y-intercepts' for the linear padding
    e = public exponent
    """
    if(len(cArray) == len(nArray) == len(aArray) == len(bArray) == e):
        for i in range(e):
            cArray[i] = Integer(cArray[i])
            nArray[i] = Integer(nArray[i])
            aArray[i] = Integer(aArray[i])
            bArray[i] = Integer(bArray[i])
        TArray = [-1]*e
        for i in range(e):
            arrayToCRT = [0]*e
            arrayToCRT[i] = 1
            TArray[i] = crt(arrayToCRT,nArray)
        P.<x> = PolynomialRing(Zmod(prod(nArray)))
        gArray = [-1]*e
        for i in range(e):
            gArray[i] = TArray[i]*(pow(aArray[i]*x + bArray[i],e) - cArray[i])
        g = sum(gArray)
        g = g.monic()
        # Use Sage's inbuilt coppersmith method
        roots = g.small_roots(epsilon=eps)
        if(len(roots)== 0):
            print("No Solutions found")
            return -1
        return roots[0]

    else:
        print("CiphertextArray, ModulusArray, and the linear padding arrays need to be of the same length," +
         "and the same size as the public exponent")

def LinearPadding():
    import random
    import binascii

    e = 3

    nArr = [
        0x81e620887a13849d094251e5db9b9160d299d2233244876344c0b454c99f7baf9322aa90b371f59a8ed673f666137df1f1e92d86e7b036479a2519827a81c7648543e16d4d0a334d0aa1124ad4c794298c3a227abfe1d44470ad4649609630450cb83f42f68ff2c445aaf546483b7a2b0a6e5877634ace5e640f8d8cbdc6a379,
        0x6c7c7935c58a586cf45e2e62ee51f6619ae2f6a7cef3865ed40a0d62ec31ba612e81045bcc6e50aa41d225b0f92b0d4a40051e2cf857ba61e91619e8fb3e2691d276c1abb5231c8012deb449e85752d2a02119bb186da6f7d41d704261284b395eec17ed4a2b07d1b97e34db8164e3093dd6cffbb0119ef8b3e9e960b0d96d05,
        0x5e67f4953462f66d217e4bf80fd4f591cbe22a8a3eac42f681aea880f0f90e4a34aca250b01754dd49d3b7512011609f757cbaf8ae7c97d5894fb92fb36595aff4a1303d01e5c707284bbfdc20b8378e046650675353e471853fa294f779df7b1b3f7cbe1748c2109d22cea682b01cb2c7719df03783e66cc3e44889a002c517]
    cArr = [
        0x3512b763bab0b45b2c6941cccd550c8b2628cea0f162dc3902951e48115d58d16ea25075da6331617e7a4ac6062190f8ce91c65c91cff57a845a21d2ebd792b46bdcb666bc4aeab2232f990956084003b652664444ba0255dbab16620b2b232a1a4e6ec04e24249ff7ba33c70cb98c50d1f46bed076c53e2c95d0ec7dee5ad2f,
        0x36bfe6fba6f34b93a0d2d44c890dfe44afc715a586bc1a44aa184571bb88a238187024b36b22a1f52a64f553fb52cf7ce193937e047307dd62e4c980601a3d20b1fbfe69888992726b11bf20330e48e4a64c6d4825d1c6d058d745f5a709c2ab5ac86da1feacf13e9de2237426b70a17a56d201b4743c68b70fdd4c7ce5eaa3,
        0x4961ba65469dfc17e663af04dfb8eeee16c61df4f85971495d0c7e7061040602638963651791cfad28992312309c3179da27babf2a80fe41c062b21aa922da53bd793c614a0974ec5e5e18f9696df875e98aceef17d476d7615ea304e7e9869696711016151666f6b58f31241c590b3b313009434b444bcb7694bb8309d89475]
    aArr = [
        0xd0f458bc246d88f38e78076b36ad58981928594035b9e428401dc3ccf049a8012926dffb5be9fa225e8e128370581acc79ee24fa259d4ea895ce61d3d607ed2b,
        0xfbedf9c34170262e2ed0eee7512e935715400a8ce541285c98e5269d2cdf4dc1aa81e117bf5d62a3310064376e8c3d5d5c4fa67e5a434ad93e5875eaa7be9545,
        0xa2995200a4f252d7ba9959a3b7d51c4b138f3823869f71573f4ab61c581ce8879d40396a33ddc32a93fd100a1029dba53e41a0acbe9e023a0bf51c6e4ddc911d]
    bArr = [
        0xc2a6d47dc16824c86e92a9e88a931d215846052fe6787c11d0fcd9f4dde28f510707c33948290f69644a7fa64075d85e7761cfff3c627ee5156a03bd9f241c51,
        0xc2343fdbb6a351b387174db494e03d0879bea084e65b16f3f0ad106472bd3974813aec28a01fcceeae00db6d38b6c32bb6ce900dff236ae9c5814ad089591115,
        0xc4a2fb937c7441be58bfcb06208e0987423ab577041d0accf1f446545b9ebb7e4874fc56597ab1b842bb50e364a62f07a0afe7d6eff7a805361f8d3a12e79d65]
    randUpperBound = pow(2,500)

    msg = linearPaddingHastads(cArr,nArr,aArr,bArr,e=e,eps=1/8)
    msg = hex(int(msg))[2:]
    if(msg[-1]=='L'):
        msg = msg[:-1]
    if(len(msg)%2 == 1):
        msg = '0' + msg
    print(msg)
    print(binascii.unhexlify(msg))

if __name__ == '__main__':
    LinearPadding()

2.exp.py

HOST = "47.240.41.112"
PORT = 54321

from Crypto.Util.strxor import strxor
from pwn import *

def pad(msg):
    pad_length = 16 - len(msg) % 16
    return msg + chr(pad_length) * pad_length

r = remote(HOST, PORT) 
ru = lambda x : r.recvuntil(x)
rl = lambda  : r.recvline()
sl = lambda x : r.sendline(x)

# Give a large number bigger than n to break proof_of_work
ru('{65537, ')
n = ru('L}').strip('L}')
n = int(n[2:],16)
ru('Give me something you want to encrypt:')
sl(str(n**2))

# pad the message and target message we got in the first step
msg = pad("I will send you the ticket tomorrow afternoon")
target_msg = pad("I will send you the ticket tomorrow morning")

ru('message')
sl('1')
ru('this:')
message = ((ru('n').strip(' ')).strip('n')).decode('hex')
ru('message')

# message xor enc_message = middle_key_stream, middle_key_stream xor target_message = enc_target_message, so enc_target_message = xor(message,enc_message,target_message)
enc_target_message = strxor(strxor(target_msg,message),msg).encode('hex')

# choice 2 and send enc_target_message to get flag
sl('2')
ru('now:')
sl(enc_target_message)
flag = ru('}')
print "[+]FLAG IS: "+flag
r.close()

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