The ARX operation is a general term for the following three basic operations. - Add Modification on the finite field - Rotate circular shift - Xor XOR
There are many common block cipher algorithms that use only these three basic operations in a round function. Typical examples are Salsa20, Speck, and so on. In addition, [IDEA] (./idea.md) also uses a similar basic operation to construct the encryption and decryption operation, but replaces the shift by multiplication.
Advantages and disadvantages¶
- Easy operation and fast operation
- Execution time is constant to avoid time-based channel attack
- The combined function is sufficiently expressive (see example below)
- Among the three basic operations, Rotate and Xor are completely linear operations for a single bit, which may cause some vulnerability (see [Rotational cryptanalysis] (https://en.wikipedia.org/wiki/ Rotational_cryptanalysis))
2018 *ctf primitive¶
This problem requires us to combine a certain number of Add-Rotate-Xor operations, so that the obtained encryption algorithm can encrypt the fixed plaintext into a specified random ciphertext, that is, construct an arbitrary permutation function through the basic operation. The flag is obtained after 3 successful builds.
For the operation under modulo 256, a typical ARX-based transposition operation can be expressed as the following combination
The above function corresponds to a permutation operation that swaps 254 and 255 while keeping other numbers unchanged.
Intuitively, since the carry occurs in the modulo plus 2 operation of the first step, only the input is 254, 255, the combined function can treat this situation differently.
Using the above atomic operations, we can construct a permutation of any two numbers 'a, b`. Combined with the Xor operation, we can reduce the number of basic operations required to meet the limitations given by the title. One possible operational step is as follows:
a, b, make
a0 by modular operation
- Move to the right by making the lowest bit of b
bis not 1, perform the
Xor 1, Add 255operation, keeping
astill 0 and decreasing the value of
- Repeat operation 2-3 until
Add 254and transposition operations, exchanging
- For all operations except transposition, add the corresponding inverse operation to ensure that the values other than
a, bare unchanged.
The complete solution script is as follows:
from pwn import * import string from hashlib import sha256 #context.log_level='debug' def dopow(): chal = c.recvline () post = chal [12:28] tar = chal [33: -1] c.recvuntil(':') found = iters.bruteforce(lambda x:sha256(x+post).hexdigest()==tar, string.ascii_letters+string.digits, 4) c.sendline(found) #c = remote('127.0.0.1',10001) c = remote('184.108.40.206',10001) doped () pt='GoodCipher' def doswap(a,b): if a==b: return if a>b: tmp=b b=a a=tmp years =  ans.append ((0.256-a)) b-=a a=0 while b!=1: tmp=0 lo = 1 while b&lo==0: what << = 1 tmp+=1 if b==lo: ans.append ((1,8-tmp)) break if tmp!=0: ans.append ((1,8-tmp)) b>>=tmp ans.append ((2,1)) b^=1 ans.append ((0.255)) b-=1 ans.append ((0.254)) for a,b in ans: c.sendline('%d %d'%(a,b)) c.recvline() for a,b in [(0,2),(1,7),(0,255),(1,1)]: c.sendline('%d %d'%(a,b)) c.recvline() for a,b in ans[::-1]: if a==0: c.sendline('%d %d'%(a,256-b)) elif a == 1: c.sendline('%d %d'%(a,8-b)) elif a == 2: c.sendline('%d %d'%(a,b)) c.recvline() for i in range(3): print i m=range(256) c.recvuntil('ciphertext is ') ct=c.recvline().strip() ct=ct.decode('hex') assert len (ct) == 10 for i in range(10): a=ord(ct[i]) b = ord (pt [i]) #print m[a],b doswap(m[a],b) for j in range(256): if m[j]==b: m[j]=m[a] m[a]=b break c.sendline('-1') c.recvuntil('Your flag here.\n') print c.recvline()
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